I think telling it is only part of processing--but a really important part, at least in trauma work. And each time we tell, it's a different experience because of the way memory and emotion and situation interrelate. Plus there's the effect of hearing ourselves, which changes each time. Allowing our Ts to witness this evolution can be the basis for more helpful responses.

ETA: And yes, it is humiliating and painful, as well as cathartic and empowering.