I think you're talking about slightly different things.
The issue (which I agree with) is that the month and date "share" a continuous grey background which makes them seem connected.
They can be visible at the same time, but it would make sense to me to separate the backgrounds as to indicate that they can be scrolled separately before touching them.
Ok, I see. Yes I do agree that having some visual indication of independence of month from year would be better than none.
Although in this case since the only thing you can do is try to touch and move something, it only takes one "not sure what this does-touch" action to discover that they are independent; and then you know how to operate it. Not ideal, but low on the pain scale.
I'm not suggesting that they are stuck together; that would be pointless.