I worry your third paragraph is mostly correlation: conditioned on someone being able to do a lot of push ups they are likely to be healthy and active rather than just someone who trains push ups.
I am pretty sure that the firefighters in that 10y long study are already likely to be healthy and active. But your argument is sounds and it's only one health study, so I should have said correlated.
But in my defense I used the same terminology as the article I linked to.
edit: I did not used the terminology from the articles but I said correlated instead of predictor... I should have re-read my post before replying... anyway I agree with you ;)
