Black holes, information, and "fire walls"

It's not my area, but I always take notice when part of the physics community is abuzz about a thought experiment that seems to expose flaws in our understanding.  At issue is whether something dramatic (involving quantum gravitational effects) takes place at the event horizon of a black hole, from the point of view of an infalling observer.  Way back when I took a general relativity course, I learned that, because of the way spacetime works, the more massive the black hole, the more mild the actual curvature of spacetime at the horizon.  Tiny blackholes = tightly curved spacetime at the horizon; galactic-mass blackholes = nearly flat spacetime at the horizon.  (The horizon is the location where, in the usual Schwarzchild treatment, the sign of the metric components flips; that's another way of saying that once you cross the horizon, classically you are inevitably going to hit the singularity.  Avoiding it is mathematically as hard as avoiding next Tuesday in flat spacetime, as my professor had said.)  So, the old-school classical picture says, a freely falling observer can cross the event horizon and not even realize it.  Moreover, classically, an observer at rest relative to the black hole outside the horizon never actually sees anything cross the horizon - from such a perspective, a clock falling toward the horizon gets progressively more red-shifted and runs slower and slower, stopping altogether at the horizon after being infinitely red-shifted.

I freely admit that I don't understand Hawking radiation beyond a handwave level.  Still, I would be grateful if someone could explain to me, even more clearly than the article linked above, what the big deal is.  Arguments about entanglement across the horizon sound almost theological to me - if it's by definition impossible to check to see if measurements inside the horizon are quantum-correlated with measurements outside the horizon, then such discussions don't seem scientifically meaningful.