I think they may be referring to a c-section which is major abdominal surgery (speaking from personal experience).
Yup, my wife had a C-Section for all 3 of our kids. (First one was breech, and the doctor doesn't do VBAC's).
Either way, I agree. *IF* the parents want to videotape it, and the hospital says no, they can go to another hospital. That's the free market we have.