To answer this, we have to know what "knowledge" means.
One answer is to take the radical skeptic's approach to say that we can know nothing, but that doesn't quite fit with the line of questioning you're after, so let's narrow the definition to assume that knowledge is something that can indeed be obtained.
The most common criteria for knowledge in philosophy is "justified true belief" (JTB). This set of criteria is typically chosen because it captures what people tend to believe is true about "knowledge," but is still generalized enough that people with widely varying definitions can still get behind the criteria. Presenting these in the order SEP presents them in the link above:
- True - Knowledge must be true. You can't know false things. By these criteria, you cannot know that you are holding a royal flush in your 5 card poker hand if you are actually holding 2 pair.
- Belief - You must believe something for it to qualify as knowledge. You cannot know you have a 2 pair if you actually believe you have a royal flush. You may actually be holding the 2 pair (it's true), but you don't know it unless you believe it too.
- Justification - You must have a reason behind that belief. If your cards were dealt to you face down, and you happen to have 2 pair, you don't know you have 2 pair, even if its true and you believe it, until you have a justification such as "I looked at the cards, and saw two pair" or "the dealer's a known card mechanic, and he's going to deal me 2 pair to make sure he wins this hand" or even "I used a dowsing rod over my face-down cards and the energy from the rod says it's two pair."
Note the flexibility in the justification. People often disagree over what qualifies as a justification or not. Sometimes those disagreements are violent, especially when the disagreement includes religious aspects or household chores. And it is this justification that is key for exploring your question. Your wording suggests that some knowledge may be "better" than others, relating to how you know it.
Now you ask if knowing only "roofly" knowledge is fine. You describe "roofly" in story form, rather than defining it, so forgive me if I capture it incorrectly. I believe what you are talking about is knowledge whose justification is not rooted in a chain of knowledge which leads all the way down to the most fundamental knowledge -- the root of all knowledge.
And the answer is: what is the root?
2+2=4, right? You know that, right? How do you justify it? Well, if you want to take the "fundamental" approach, this can be phrased in a more fundamental language, that of Peano arithmetic,
Su(Su(0)) + Su(Su(0)) = Su(Su(Su(Su(0)))), where
Su is the successor function and
0 is defined to be a number, zero. You can then use the laws of Peano aritmetic to demonstrate that this statement is true. It is now more fundamental.
But note that I just used something new. I used the "laws" of Peano arithmetic, and implicitly I assumed there was a way to turn this into a proof (proof theory). Those are not fundamental concepts, are they? We have to dig them further. Now it turns out, in the case of proof theory, it pretty soon reaches the point where we have to admit "we don't know how to make this any more fundamental." Proof theory is one of the more fundamental subdisciplines within mathematics. From there we can start to delve into philosophy, but we quickly find this issue becomes complicated there.
I mentioned the radical skeptics earlier. One of their claims is known as the Agrippan Trilema or the Münchhausen trilemma (depending on whether you give credit to Sextus Empericus from the 2nd century or Hans Albert from the 20th). The trilema argues that proofs must always lead to at least one of:
- A circular argument - an argument which can only be proven true by assuming it is true.
- An infinite regression - an argument which assumes that you can keep repeating an argument ad infinitum (in mathematics, this is called mathematical induction)
- An unproven axiom - A statement which is simply assumed to be true, without proof.
Generally speaking mathematics is only really comfortable with the last one. You are permitted to define the axioms for your proof, and then use them. If you want infinite regression, you typically must include an axiom which permits it (Peano arithmetic includes a 2nd order axiom which permits us to use mathematical induction). Circular arguments are tremendously unpopular.
Which leaves us tugging on unproven axioms. While the radical skeptics can't claim they know that all proofs will end up in this trap (for consistency) one has to appreciate the rabbit hole which occurs when trying to keep digging all the way down. Where does one go?
So given that, I would say the answer is that you cannot gauge the usefulness of an approach to knowledge (roof to floor, floor to roof, or otherwise) based on whether it starts from a "root" or not. It's so hard to define a root without opening a new can of worms.
So what else might we try? We might try "rooting" in reality. Many approaches take this. The martial arts I practice have a tremendous amount of abstract thought that goes into them, but my teachers are always quick to focus on what is done in reality, not what is done in the world of language. Quite often the clever corner I stuck myself in with language simply doesn't exist in the real world!
But how did I learn that language? Surely it was through my many years of real life experience, teaching me to hone my tools better and better (the floor to roof like approach). Surely this language is just one more part of reality, is it not?
So that suggests it's difficult to say that knowledge needs to be rooted in reality -- the definition of that is just as slippery as anything else.
A final line I enjoy looking down: what if we revisit the idea of circular logic. Mathematicians like Kurt Gödel explored proof systems which can reference themselves, self-referential proofs. This opens a whole pandora's box of issues. Sentences like "This sentence is false" need to be carefully teased apart according to consistency. "This sentence is false" is inconsistent, so cannot be included in any consistent system.
Gödel penned his incompleteness theorems, which put some brutal limits on self-referential proof systems. Handwaving greatly, they basically showed that consistent self-referential proof systems cannot be strong enough to prove all the laws of arithmetic. So if we permit circular logic, we have to be very careful with how powerful of a proof we try to make, or it will be inconsistent.
But what if the answer is we need to stand on our head. What defines the "root" anyways? I've implicitly defined it as a fundamental true theorem from which all else spawns forth. But I've also pointed out that "root" might mean "rooted in reality." What if we "root" it in the sky?
Dan Willard explored a wonderful little set of proof systems to try to get around what Gödel proved. He relaxed one rule: he did not assume multiplication had to be total. This means there may be two numbers which cannot be multiplied together to get another number. Those may not be finite numbers, mind you, they may be infinite -- but he doesn't assume that all numbers can be multiplied. He then starts with the universe. He starts with a universal set containing everything, and defines arithmetic by subtraction and division rather than addition and multiplication.
The result is a system which sidesteps some of the tools that makes Gödel's theorems work, so he can create a system which proves all statements of arithmetic (except totality of multiplication) and is self-referential. It's beautiful math.
So what's the point of that? I'd argue that it's just more evidence that the definition of "root" is fuzzy. Willard defined the root to be "everything." And he got results. Are his results better or worse than Gödel's? Are the results of these famous mathematicians better than the results of my martial arts teacher, who is less famous?
To close, I would like to address your last question. "Almost the same" is a very fuzzy phrasing, but what I think we can say is that it is remarkably hard to define a metric for what methodologies for knowledge are better than others. This is why school systems still struggle with curriculae, even though we've been schooling for hundreds of years. Each metric has it's own quirks, and whether that makes them better or worse quickly becomes a personal question. I personally prefer to build up from mathematical fundamentals, because it tends to work for me. However, I cannot argue that it is the "right" way for others. It's just the approach I take. To each their own.