Evidence points to it being true, all other things being equal.
As you clearly state.
This gives us a high probability of being objectively true.
Just because you can't admit the truth doesn't make it untrue.
The limitation appears to be yours. You can't even admit that a thing is what it is -- the most obvious truth imaginable.
High probabilities are not objective proof. Indeed, there are plenty of examples -- both ways -- to demonstrate that "good nutrition" is neither necessary, nor sufficient to ensure good health. And of course, the definition of "good nutrition" is itself a rather subjective thing.
Just because you can't admit the truth, doesn't make you any less wrong.