I've witnessed this myself, many times. I honestly find the proficiency of iPad finger gestures in children < 2 to be shocking. It feels like I'm viewing some real world parody with how quick and controlled their hand motions are as they navigate through the interface. It really gave me a new appreciation for just how intuitive the UI is for someone with zero technical literacy... or any form of literacy for that matter.
I had one family tell me they learned about five finger swipes from their 1 year old daughter.
My daughter is 3 and learned to use a phone/tablet before she was 2. Whenever I'd pull up YouTube on my tv she'd walk to the tv and try to swipe it as well. Often getting upset thinking the tv was broken, haha.
She was used to iPads, but one day I gave her my Android tablet. She was upset at first because things are slightly different, but adjusted quickly. I was shocked at how fast she picked it up.