It is far easier to understand in terms of tunneling. I explained it this way to someone on another board some time ago:
You probably know that quantum mechanics predicts that systems like atoms have energy levels. So, the hydrogen atom has a lowest energy state, a first excited state with higher energy, etc. but nothing in between those energies. It works in much the same way if you apply quantum mechanics to fields. What you find is different series of equally spaced energy levels. These energy levels are interpreted as states containing particles of various energies. I.e. particles are just excited states of fields.
Now, just like if an hydrogen atom is in its ground state you can't say that there is no hydrogen atom, the same is true for fields. If the electromagnetic field is in the ground state, then that means that there are no photons, but the electromagnetic field is still there. Now, I think you have read about quantum tunneling. Suppose, e.g. that you have a system that has three quantum states: X, Y and Z and that in X and Z it has the same energy while in Y it has a larger energy. If the system, when described classically, can only go from X to Z while passing through Y, then it cannot make that transition because that would violate energy conservation.
But according to quantum mechanics such transitions are possible. The fact that a "real" intermediary state Y exists connecting X to Z is enough to make transitions from X to Z possible, even though the system cannot be found in state Y because of lack of energy. We can qualitatively say that the system goes from X to Z by first making a virtual transition to state Y (by borrowing energy using the time energy uncertainty relation) and then from Y to Z and then paying back the borrowed energy used to make it to Y. What is crucial here is that X and Z do have the same energy, so energy is conserved.
In case of virtual particles it is much the same story, the intermediary state Y being an excited state of a field (i.e. a particle) for which there is not enough energy, but which nevertheless couples an initial state X to a final state Z. So, in case of the evaporating black hole you have:
X = black hole has energy E, field is in ground state and has energy zero.
Y = black hole has energy E, field is in an excited two particle state with energy 2q
Z = black hole has energy E - q, field has energy q, i.e. there is a particle with total energy q.
Clearly X and Z have the same energy: E = E -q + q. But Y has an amount 2q more energy. The transition from X to Z is still possible via quantum tunneling via Y. If the system had enough energy it could have made it to Y and paid for the two particles of energy q each, then it could have let one particle crash into the black hole and let the other escape. So, the state Y does indeed connect X to Z.
Because we don't have the 2 q of extra energy to pay for the two particles, the state Y is entered virtually with energy zero. One can then assign a total energy of zero to the two particles. But note that we already know how state Z must look like: Black hole ends up with energy E - q and the particle that escapes has energy q. You cannot write down a final state Z in which the black hole ends up with energy E + q and the escaping particle get's -q, because the field has an energy of zero at least (the ground state is the lowest energy the field can have).
No, by "accurately predicts.." you probably just meant "consistent with other thought experiments from thermodynamics"? 
