Oh dear oh dear oh dear.
There is some genuinely sound advice on this thread (on both sides imo), and also some rather unnecessary unpleasantness, which is a great shame but it happens every time this sort of topic comes up.
I wish people wouldn't get so judgey about other people's birth plans. I don't want a homebirth (for instance) but if that's what someone else really wants, I'm rooting for them to get it! In this case, the poor girl is clearly so terrified, I think it's more than a fancy or a whim.
Fact is, people have terrible experiences of VBs and terrible experiences of sections, and the reverse. Yes, there are risks of various things with both kinds of birth. Yes, the risk of maternal death is higher with a cs but it's still (thankfully) a tiny tiny fraction. Some people are happy taking the extra risks of a cs and some aren't; so what? Do we really need to beat each other up about it?
If people don't get the kinds of births they expect it's often a surefire route to PND and I really wouldn't wish that on ANYONE. Everything else aside, I think the OP should definitely try the counselling, not to 'change her mind' necessarily, but to try to ease her marauding anxiety.
I wish everyone the births they want, and hope that Mum and baby come out healthy at the end of it. I'm certainly not going to rag anyone for anything, whatever they choose. Jesus, it's hard enough however you do it, ain't it?