Given her age, I'm going to make some assumptions about her friends --
1. If any of them have given birth, they are likely to have been heavily managed by the hospital staff/OB during said process, and fed a lot of lies (it seems that is more likely with young mothers).
2. They don't know much about birth and rely on media etc. for their information (and we all know how supportive the media is of NCB).
3. They also find the whole birthing process a bit freaky and foreign, so they are joking about it to try to get past that.
....If I were you, I'd post something light-hearted under their comments, that you think your cousin would recognize as supportive of her choices .... Maybe something along the lines of, "I used to worry about that - but two kids later, I know that a woman's body is amazingly capable when the time comes!" Or etc.

And keep reassuring and supporting her IRL.
When I had a similar conversation with a friend's friend who was pooh-poohing breastfeeding, we actually ended up discussing it via email ourselves, and I was able to tell her how important the support of my friend who hadn't breastfed was, when I was struggling - that we owe it to our friends/sisters to help them do the best they can and not assume they'll fail.