The concept I was missing was that testing two different random variables at the same time (do meat or vegetables affect telomere length in this group) has the

The concept I was missing was that testing two different random variables at the same time (do meat or vegetables affect telomere length in this group) has the same probability of yielding a false positive for one of the variables as testing the same variable twice (does meat affect telomere length in this group, does meat affect telomere length in that group) has of yielding a false positive for one of the tests.