I feel like I'm missing something in the question. I think you're asking: "Is it possible for a sentence to be true, even if nobody believes it?" If that's not right, let me know and I'll try again.
There are a variety of theories of truth, and they would offer different answers to the question you've posed. Let me mention just three such views:
- The correspondence theory of truth says that sentence is true if
and only if the world is the way that the sentences says it is, i.e.
if the world corresponds to its representation.
- The coherence theory of truth says that a sentence is true if and
only if it coheres with the rest of our beliefs.
- The pragmatist theory of truth says that a sentence is true if and
only if a community of ideal observers all in the possession of the
complete evidence would say that the sentence is true.
On the correspondence view, it seems most plausible to think truth is utterly unconnected with belief. Since the world is the way it is independent of our beliefs about it, therefore sentences about the world are either true or false, regardless of whether we exist or not.
On the coherence view truth definitely would require belief because for a sentence to be true is, as it were, for that sentence to be connected to other sentences we take to be true. Coherence theorists must reject the idea that there could be truths which nobody ever in principle could know.
On the pragmatist view of truth, its harder to tell. Some pragmatists, such as Susan Haack and Cheryl Misak (I think) want to suggest that the pragmatist view of truth turns out to be very similar to the correspondence theory in point of fact. So, I take it that these pragmatists also wouldn't necessarily have a problem with saying that a sentence could be true even if nobody in fact (at the present time) believes it. However, like correspondence theorists, they would want to reject the idea that there could be a truth that nobody knows.
Now the curious thing about the literature on truth is that there aren't really good arguments for each of these views. The main argument for the correspondence view is just that it seems very plausible and intuitive and fits with our pretheoretical judgment that truths about the world are discovered rather than made. (I think something like that must be what Neil deGrasse Tyson means in the quote above.) Further, the correspondence view seems to avoid important problems the other views have.
The coherence theory, for instance, seems to let too many things count as true. Imagine a really nice, consistent fictional world present in a novel. If coherence theory of truth is right, then a sentence is true if and only if it coheres with other sentences, so if the fictional story is coherent, it's literally true. In other words, if the Lord of the Rings is a highly consistent set of sentences, then there are such things as Dragons, Elves, Orcs and so on. This looks like an important difficulty for the coherence theory.
Another difficulty, which the coherence theory shares with the pragmatist theory is that it seems to require that there simply couldn't be such a thing as an unknowable truth. (Note that it's an unknownable truth. Everyone wants to say there are truths that aren't in fact known; the question is whether there are truths that nobody could know.) There's an important paradox called Fitch's Paradox that is supposed to show that actually if you hold that all truths can in principle be known, then all truths must be actually known. This is a surprising result! (Unless you take the pragmatist theory of truth to provide an argument for the existence of an omniscient God.) But furthermore, the pragmatist theory of truth faces the difficulty that there are some problems in logic and mathematics that are provably undecidable. That means that it can be proven that there cannot be a proof of certain questions one way or another. Yet, these are question in logic, so it seems like they should have answers and that their answers should be not only true, but necessarily true.
Of course, the correspondence theory faces it's own challenges. The primary challenge is to make sense of the notion of "correspondence" and to say what the correspondence between the world and the sentence is supposed to consist in.