I had a cord prolapse and my daughter died. It was obvious the cord was external to me. To be honest, I'd be grateful for the intervention on a suspicion, even if false...
The death of your baby is something you don't want to have to experience.
It was the fucking most terrible experience of my life, a true emergency. I watched my daughter dying on a scan... I too, was on hospital at the time.
I don't mean to sound trite or belittle your experience, but you baby is healthy. I have had subsequent traumatic births, 2 emcs, I no stranger to difficult births, I know nothing is as terrible as a cord prolapse (actually, holding your dead baby is the most heart-breaking thing ever).
I say this if you are planning to complain to the hospital. Pals is of course the way to go. However, I do warn you, I know women who have gone through pals to complain when their babies have died and you don't get a good outcome, just lip service.
You have a ga with a cord prolapse because it is a true emergency, catastrophic and baby needs immediate delivery.
Sorry to sound so negative but to have this experience and lost your child is such a sad experience beyond words. Counselling would be appropriate, but some end up holding their dead baby after the experience....