"The point of this is that if we provided these Ancient Greeks with nothing but urgent life-saving emergency care from modern technology, it's highly likely that their life expectancy would dwarf ours of today."

This is something you can't possibly determine. Ancient Greeks famous enough to have their own Wikipedia pages may not have had penicillin but on balance they certainly would have lived easier lives than peasants who worked years of hard labour just to survive, and would have lived longer because of it. It is also, quite literally, survivorship bias - people who lived to be older had more time to achieve things and become notable enough to make Wikipedia.

The thing with getting old, as noted in the article, is that past a certain age if one thing doesn't get ya, another thing probably will. Modern medicine is not a buff which will add +X years to all humans regardless of circumstance, it is just about staving off the first few things which try and kill you - and that's why, by all accounts (including this article), life expectancy is longer now than it was in the past.

And for the record boiling water works just fine at killing bacteria living in it. It's not magic and if your water is still full of arsenic you'll still die, but it's much better than nothing.