It's a good question, and one that most likely requires a full general relativity solution, with Hawking radiation included, to answer. Few are capable of that calculation, and those that are don't always get the same answer (witness Hawking's famous "bet"). For the rest of us, black holes are as black holes do, and what they do is act like an ultracompact source of gravity accounting for all the matter that has been accumulated at or near the event horizon. I think the problem at the core of your question is that what we want, out here at Earth, is to know how the black hole affects its surroundings, well away from the event horizon. Thus we are not interested in local concepts of time near the event horizon, we want to stick with our own concept of time. It is known how to handle that in general relativity, but I personally have never been too clear on it-- it's mighty tricky!