Um... there are a lot of misconceptions here. I'd recommend anyone who is really interested to carefully read Hawking's book, or something similar. I'd like to try to give a concise explanation, but I don't think it would help. There's a reason that there are entire books written on this subject.
The simple answer (not an explanation!) to the original question is that time does flow differently in different parts of the universe, but even defining what that means is very difficult. Time is on the one hand a very arbitrary way of labeling events, but the fact that we all experience it identically is a clue that it does also have a very "real," invariant character. That statement can be made rigorous, but again, it takes a lot of explanation.
Also, most of the parallel universe etc stuff you read about is what I like to call PR physics. I doubt it has much relation to reality (I am a physicist myself, so I'm not talking out of my ass here). Most of those things are more properly classified as mathematical playtime than proper physics. One takes a HIGHLY idealized solution, extends it beyond the realm where it MIGHT resemble a real situation, and then uses some trick to extend it beyond where the equations would naturally "give up."
The problem is not that these people are doing poor science. Its just that in the translation from original paper(s) to scientific american article, the focus/purpose of the work is completely reworked.