The thing is, there is no suggestion in the article that the baby was actually in any danger. The issue of a woman refusing intervention while her baby dies inside her is a completely different issue to what the woman in the describes happening to her, that healthcare professionals repeatedly lied to her and performed an operation on her with no reason, discussion or consent.
It does sound like she was very keen to get a VBAC and so changed doctors when their initial positive support turned out to actually be lukewarm, but that doesn't mean she should not have been lied to about what was happening several times, and told to breathe "oxygen" when it was in fact aneasthetic. That is appalling.
My cynical side says that the HCPs looking after her thought she was trouble and would not do as she was told (which, to be fair, she may have been and may have done), so made a decision not to give her a chance to object to what they thought was best for her and her baby.
Yes, it is hard to believe that HCPs would do something invasive to a woman in labour that is not medically required, but the evidence is there in that different hospitals with similar patients have widely different rates for episiotomy and cs. Either some hospitals are doing these procedures unnecessarily (or have policies that lead to these outcomes unnecessarily) or the other hospitals have magic labour fairies that somehow magically make things work out better.
The term birth rape is shocking but I can see how you might compare your feeling of being violated against your will during birth to rape.