Why would it behave differently with 16:9 and 4:3 videos?
I only have an older iPhone with a 16:9 ratio, so I can't test what happens with 16:9 material.
But if I do the double-tap you describe on 4:3 material, it will zoom-in and crop the top and bottom.
But that's not the default behaviour in my case. I actually didn't even know about the double-tap thing.