I just showed this story to DH, he and I recently had our second child and she was held in the NICU for a time.
I can't see a hospital denying access to a baby, or babies in this case, in the NICU. We were admitted 23 1/2 hours a day, they asked us to be outside only during shift changes. Yeah, there were security measures. We had to show our bracelets and all that, though eventually the nurses knew us well enough to open the door and let us in, but even when they had a transport team in there they didn't ask us to leave or anything. They asked that, when they were physically moving the baby, we stay where we were, but never to leave.
However, if it is true about the dad being kept in or out, well, in the words of my husband "I don't care if you're a superstar, the richest man in the world, or even the flippin' president, no one is keeping me from my child and if private security guards (DH is one) think they have that power I'll get the police there to give them a reality check".