The GP wasn't saying heavy lifting is required for strength gains, he was making the much stronger claim that it was necessary to be healthy. (Perhaps unintentionally; I'm not sure they actually read the bloody linked article.)
I see the distinction you were making, but this study has an interesting conclusion[0].
"Muscular strength is inversely and independently associated with death from all causes and cancer in men, even after adjusting for cardiorespiratory fitness and other potential confounders."
That's still looking at things the wrong way round. Even in your quote, it mentions the need to control for things like cardiorespiratory fitness.
The conclusion that muscular strength will always improve your health does not imply that other things are useless! (And note that the linked routines does attempt to improve muscular strength, but the whole point of it was to be something you could do without special equipment.)
