You are completely right about ambiguity, and that's probably a problem at many levels, mostly related to our subjectivity.
I will address, as an example, thermodynamics. Thermodynamics describes the behavior of energy in a system. It means that a system (made of parts) has energy. Take note of this: a thing, made of smaller things, has energy. But that's not evident (and in fact, that's somehow naive) for a physicist (with a critical mind): in real nature, there are no THINGS. On the real nature, there's an equivalency of things made of mass and energy. Modern definitions of quantum systems define things as portions of space.
(If you haven't read the philosophy classics, perhaps you are not aware that some philosophers - leaded by Immanuel Kant - think that space and time are just mental constructs, they are not real (they are called_ knowledge a priori of experience _). I firmly believe such point of view. I once thought that Einstein would be destroyed if he would discuss relativity with Kant. Einstein was once defeated by Bohr, and perhaps Bohr will agree a lot with Kant. But that is just a personal speculation, ala Bukowski vs. Hemingway). Then, in such case, what would a quantum system be? Just a representation of sensible facts held somewhere in the brain.
Then, perhaps only the first law (energy conserves) is correct, but only if we consider that the THING containing such energy is something that we bound subjectively (what are the real limits of a balloon of gas, since the the quarks of both THINGS can hardly be differentiated, and when elementary particles are essentially empty space?). The second law would be useless (energy spreads between the parts of the whole), since energy just changes of form, we see things, but that's just our perception. The third law (entropy is 0 at 0K) is our way of saying "hey, here's the point where energy ends and mass starts", while that's clearly subjective. And the zeroth law (temperature is a transitive (comparative) relationship) is just a way of formalizing... a feeling. Yes, temperature is a feeling, there are no hot atoms or molecules. Then, thermodynamics is the scientific description of a feeling ("dynamics of temperature"). Plank died (and accidentally solved the essential problem in quantum physics) trying to prove that thermodynamics was a fundamental fact of nature, and trying to prove that Boltzmann was wrong. Well, thermodynamics isn't a fundamental fact, so whatever Boltzmann says is irrelevant at a fundamental level.
Kant said that we cannot know the truth (you assume that every theory can be interpreted subjectively, and that's a consequence). Because our interface with the real world are our senses. And so, Kant states that we live in a complete tautology: there's no final rule able to validate other rules. Our senses tell one thing (what Kant called phenomena), and math tells a different thing (noumena, reality, what we don't have access to). But even math is built over such tautology. Perhaps now you can understand why it could be possible that the work of Einstein would be applicable only to the result of our sensations.
Worst even, boltzmann thermodynamics is clear about that (boltzmann addresses THINGS), but few people pay enough attention: macrostates are what we perceive, the phenomenon, and microstates address what seems to happen down there (the noumenon). So, statistical thermodynamics assume the existence of things, by converting massive behaviors into static ("statistical") and constant perceptions. Entropy can be a flat curve only at a statistical level. In reality, it would be similar to the output of a seismometer (of course, at a hugely large resolution).
So, here's my personal conclusion: Science is built over the result of our perception (the phenomenal reality), using math, which can provide us access to the noumenal reality (which is inevitably subjectively-interpreted). But we haven't been careful enough to make a clear difference between the science that depends on our perception (thermodynamics) and the science that takes our subjectivity into account (quantum mechanics, which considers the subject, us, the observers, and the object... well, if a fundamental particle can be named an "object"). Perhaps the incompatibility quantum mechanics/gravity lies there (https://www.space.com/32147-why-is-gravity-so-hard-to-understand.html).
So, any mathematical statement is inevitably subject to interpretations. But there's no final truth: we exist, understand, think and make science upon Kant's tautology. We can create rules to validate other rules (e.g. this is science because it was developed using the scientific method). But there's no final rule that would be able to validate that.