And also with that baby still being on a heart/breathing monitor, an alarm would have sounded if anything got out of whack(faster heartrate, odd breathing pattern, etc).

I doubt it was even a rat, as I know my rats would probably lick the inside of my nose and then go on to find a place to sleep. I would think these people would be aware that their baby's room is infested with rats, hungry, flesh-eating rats at that...

Maybe it was their RAT Terrier