For a white hole horizon, you are classically smooshed on the edge until the explosion, while for a black hole horizon you fall through. In time reverse, for a black holeblack hole, you fall through, and stuff coming out is redshifted.
The idea that black holes cannot form is the analog of the argument that white holes cannot form by collapse. This doesn't matter, as when the black hole has been sitting there for eons, you can't tell whether it's a black hole or white hole. These things are only made clear once you accept Susskind complementarity.
Mooshing on horizon
The mooshing on the horizon picture is only valid for a proper time that terminates for an infalling observer. The observer is redshifted to oblivion, and merges with the BH horizon (in an exterior picture) after a finite proper time.
But in the observer's local frame, there is nothing singular for an extremely long period of affine parameter as the path becomes null. The argument that a black hole has an interior requires the assumption that when the final explosion is far away, the Hawking radiation behaves semiclassically, it becomes invisible for the infalling observer, so this observer falls through. This is a little bit of a religious point of view in the classical world, because there is no evidence for the interior beyond what you can see in the exterior, but it is justified by the consistency of the quantum picture it gives.
Without knowing that the local equivalence principle holds at the horizon, the argument for Hawing evaporation becomes suspicious. You can use the t-independence of the BH to make what is called a "Boulware vacuum" which is nonradiating, because it conserves the t-notion of energy. This Boulware vacuum was believed to describe QFT around black holes for a long time. It corresponds to the spacetime around a Schwarzschild black hole which is surrounded by a perfect ideal mirror for everything at (R=2M). This thing is thermodynamically ridiculous in the usual picture, the mirror absorbs thermal energy and doesn't heat up to equilibrium. But this Boulware idea is resurrected every once in a while, in t'Hooft's idea that the black hole has double the correct temperature, for example, because the interior and exterior are identified by a gluing map.
The evidence for the falling-through picture, which is Susskind's, comes most persuasively from the quantum theory. It is this picture that produces AdS/CFT. Without it, it is impossible to understand how black holes become so regular and ordinarily quantum in the extremal limit, where the horizon is still present, but the Hawking radiation goes away.