What you've stated is not objectively true.
The preponderance of evidence suggestst it, but the fact is that there are healthy people with wretched diets, and sick people with good diets. While I agree that the preponderance of the evidence points to a corellation, it is also clear that diet is not the sole basis of good health.
Also, it is a fact that what is a good diet for person A, may be deadly for person B. So you're left having to define "good diet" on an individual basis -- which rather inhibits your ability to define for us an objectively "good" diet.
I'd say that your "objective" basis, isn't.
Much like the rest of objectivism.
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.