These answers giving Hilbert's (and I believe Einstein's) viewpoint(s) are interesting, but perhaps there is a simpler way of expressing the issue: if time "stops" at the event horizon, then the local timelines actually truncate at a finite time before anything actually reaches the event horizon.  
Taking this a little further, this would imply that the event horizon never quite forms.  this is the same as saying that, in external time, the black hole never fully forms.  This would remove any mystery about the growth of a black hole: the near-black-hole within a certain radius is simply tends towards its limiting mass, and growth merely adds a contimuum of new layers around it.  Clearly, this description as worded applies only to a Schwarzschild hole, but the extension to Kerr-Newman holes is conceptually straightforward.  
If this represents reality, the levels of Hawking Radiation would be pretty-much unaffected; I'm not certain what (if any) impact the non-existence of the event horizon would have on the paradoxes of that processes.
I realise that this post is rather late in the day; nevertheless, better-informed critique would be welcome.

PS - addendum following Terry Bollinger's (TB's) initial response:
If I understand it correclty, the final clause of TB's response may be the nail in the coffin of my argument - i.e.: "the absolute horizon starts as an interior point".   If I read this correclty, it implies that the size of the event horizon is expanded by the presence of mass outside the horizon.  If this interpretation is correct it would allow a "real" event horizon to arise in finite time (albeit this assumes that the analyses that gives rise to this result is properly time-constrained - see below).

However, TB also talks about "physicists' view that only the infalling viewer counts"; certainly it should be possible for the infalling viewer to come up with an accurate assessment of what it observes - indeed, the equivalence of all properly analysed viewpoints is one of Einstein's own tenets.  On the other hand, this equivalence means that any analysis from the viewpoint of the infalling viewer that cannot be reconciled with outside viewpoints is meaningless to the outside viewer - and very probably meaningless in aggregate.  Thus the infalling viewer counts only as long as its existence is meaningful; thus, it cannot be meaningful to analyse this viewpoint beyond the time that the viewer ceases to exist in an externally-consistent model.  I regard any analysis that ignores this as failing the most basic credibility test.