::::::Actually, it is good enough to say that. Per my description above, "virtual particles" aren't things that exist per se - they're a convenient way for setting up the math describing how a system transitions from one state (black hole and nothing else) to another (black hole with less mass, and a particle escaping). They show up in a lot of other places, too; Feynman diagrams make use of them when setting up the math for calculating the forces between charged particles (described as mediated by an exchange of virtual particles which are allowed to travel faster than light for short distances). 

 ::::::For more information about what virtual particles are and why they show up with certain types of analysis (ones based on perturbation theory, mostly), see the full description at virtual particle.