Well, before reading what others said in those threads, I'll take a stab.
I feel that 'It's not.' is focussing on the predicate not being right. Where 'It isn't.' places emphasis that the subject is wrong. Of course we're splitting hairs here. I don't think that there's much need for an L2 speaker to have to know the difference. (We don't and it wouldn't matter which one you used in most situations.) However take a look a these simple exchanges.
S1 picks up a bag sitting in the room and simply has a question for S2:
S1: Is this yours?
S2: No, it's not.
S1: Hmm? I wonder whose it is.
S2 is looking for his pen. S1 finds a pen and asks:
S1: Is this it?
S2: No, it isn't.
S1: How about this one?
...
Maybe I'm just making stuff up. ...

Actually, naturally the answer to both of those questions would just be 'No.'