Babies look like babies. Plus you've just given birth and are probably knackered and in a bit of shock. You got a quick look at your baby then they were whisked away and cleaned up. Then you got them back some time later. It's not like it is now where they hand the baby to you for skin to skin etc. They'd be delivered, then whisked away and kept a lot of time in the nursery and be brought to you for feeding etc.
I bet it happened quite a bit.
As an aside, when I gave birth to my first son 25 years ago, his shoulder got stuck. He came out eventually but was injured and had a cone head.
He was taken to a little bay with half a dozen other babies, so I could sleep. I'd haemorrhaged during delivery; he'd nearly died, and I was a mess. I heard what I was convinced was him crying so I got up and went to the little nursery. I stood in the doorway and looked at the babies and couldn't figure out which was mine.
Which sounds maybe a bit understandable except there were half a dozen tiny white bald babies and one nearly ten and a half pound brown baby with a full head of shiny black hair on a cone head.
Guess which was my baby?
Yup.
Yet I still stood there paralysed from I guess the trauma of the delivery, and cried because I couldn't figure out which was my baby.