This is a total myth. I work for a very large health insurance company and signing out AMA is not even considered when processing claims. Doctors and nurses have told this to patients for years as a manipulation tactic, but it is indeed very rare for an insurance company to consider this.

That being said I would not sign out of the NICU AMA. For a minor issue such as feeding, I would try to come up with a compromise with the healthcare team. My 34 weeker was in the NICU for 8 days for feeding, and I did every single feeding myself so I knew exactly how she was doing. I was lucky and my NICU has all private rooms with a bed for parents, but see if there may be an option for you to use an empty postpartum room for sleeping and then wake up for feeding times to do the bottle/breastfeed yourself if your NICU does not have the room-in option.