Conceivably, there could be some other factor that falls outside of our range of senses, that functions as a constant on a macroscopic scale in our atmosphere and under our gravity, but has a different value outside of it. We have very little data, if any real data, outside of the realm of our solar system, and precious little data outside of our planet. We've made alot of assumptions that what holds true here, holds true everywhere. There's no reason the actual equation couldn't be E/X = MC^2 where X is some factor we haven't yet recognized.
This is wrong. We have not made "assumptions" we have tested theories, there is a distinction in that. The main reason we believe these things to be true is that these theories can be tested in a predictive nature, the whole "if x then y". There is a great reason why E/X = MC^2, its the fact that if E=MC^2 then we shouldn't be able to control and predict things like nuclear reactions. If there were no universal laws, then science wouldn't be worth studying because then everything would be a special case.
Its likely a measuring error, or something to do with the quantum nature of the particles, I doubt its a fundamental flaw in one of the cornerstones of physics, but hey, you never know.
I think you missed the point about "constants".
Let me rephrase what I believe he was trying to say...
There are assumptions, scientific community is split in at least two halves regarding many of the essential theories.
It's because more than one theory can explain the same phenomena, practically it's about constants. "Constant" is a number you look up in some table where other variables you get by taking measurements. Each constant potentially presents a whole world of complex interactions, but it also can be used to hide that complexity and so to simplify our equations, and then they are just substitutes for measured or deduced quantities of unknown origin or cause.
It's just that, there is only one constant. One universal. It is the only real truth. Causality - action, reaction. Cause and effect. It's what gives you that "if x then y", and what is called "exact science". Newton law of motion for example has no constants, only causality: F= m*a, and once you confirm it indeed describes (predicts) reality then you know that relation is the actual signature of a true physical law.
And then there is quantum mechanics, contradicting those basic laws of motions. However QM is not exact science to start with, it's "statistical science", and there is no more "if x then y", no more cause and effect, but it's all about chance, probability and likelihood. It's full of constants and look-up tables, no real equations since you are not supposed to even be able to make any proper measurements according to it. Still you can get working and useful equations, but you get lots of them, with lots of constants, lots exceptions and special cases, and it's ugly.
It's similar to fluid dynamics in some way, where even though the interaction on molecular scale is rather random and very complex there is some harmony emerging from within that chaos, so as a result you can simplify a lot of it and substitute with constants without any concerns about micro-dynamics going on deeper inside.
Although not as bad as QM there are lots of constants (unknowns) in General and Special Relativity as well, but the real point here is that all of these theories contradict each other, they only work within boundaries of their own domain. It is widely believed this disagreement means all of them are incomplete and so there is this quest to find "unified theory of everything".
Only, there is not enough money to test everyone's theory, so the sad story not many are aware of, even though it is well documented throughout the history of science, is that "scientists of old" are always holding onto their positions and reputations, to the extent they are willing to label everything else as a hoax, so the real truth may very well be with some poor guy locked away in asylum. What I am trying to say here is that history teach us we should never be too sure in our present theory, even if it works and explains. It's that skepticism towards your own believes that makes you keep trying, experimenting and discovering, finding even better theories. Otherwise scientists too could just write their own bible believing they already know everything and then that would be it, the end of science.