I don't think I've made clear why the Frist/HCA/abortion issue is, well, an issue.
First, it's clear that Frist is no ideological anti-choicer, he's an opportunistic one. This is another way of saying he lies about it. Fair enough. As a pro-choice person that could be a good thing, but it also mean he's willing to play politics with women's health issues which is rather repugnant.
Second, to the extent that he's advocated for government restrictions on abortion (and he has adopted the morally unsound position that it's only okay in case of rape, incest, or the when the life of the mother is in danger), this is another example of public morality differing from private morality. It frankly isn't much different than advocating a legal anti-choice position, then driving your wife to the abortion clinic. For the First family business to be, partially, an abortion provider without him taking a public stand on the issue implies he puts profits over his morality. While I am glad that Columbia hospitals will do abortion procedures unlike, say, Catholic hospitals, this doesn't change the inherent moral cowardice, from Frist's supposed perspective.
On balance, I'd rather have a fake pro-life senate majority leader than a real one, but the anti-choice movement has had much success in recent years. In some states there are only one or two abortion providers - which means it is almost impossible for most women to obtain real health care. The rhetorical legitimization of this position, especially from someone who is essentially lying about their moral stance, is in itself damaging.