I am in the minority here in that I never minded the family video-taping or taking still shots, and would generally even try to give them an opportunity to get "posed" pics of baby in warmer, if everything was going fine. Other times during the actual birth of baby or during a resucitation I was generally explaining to mom and dad exactly what was happening, what we are doing about it, and why, for one reason saying the steps outloud helps ME remember them and talking to the parents instead of outloud to yourself just seems more professional/competent. I have never had a problem with a support person asking me to move out of the cameras way during a birth, and I would like to think this is because I have kept them informed at every step along the way.
If I were a lawyer I would be questioning why no video exists, I would bring the parents into the court room and I would ask them what was said to them regarding video, I would review the policy, I would question EVERY hospital witness regarding this policy. After all if you are practicing competently, what do you have to hide, if you did nothing wrong why would you care if video exists? If you followed standard of care then the video should exonerate the doc, the nurse, and the hosp. right? If it were altered it could be proven, and the plaintiffs would be charged with tampering with evidence, and would lose their case.....that's what I would do if I was a lawyer.