I'm not sure that the active/passive debate makes a lot of sense.
First, video has convinced me that I don't necessarily know what I'm doing in a high level of detail. I assume the same holds for a lot of the pros.
Second, I'd guess that the forearm muscles that control wrist movement are firing off when all of us play, just to hold onto the racket and to keep the wrist from collapsing back too much against the momentum of the racket and the pulling forward of the arm by much stronger muscles in the body.
As far as the use of the wrist on the serve, I'm not a fan of the term wrist-snap. However, "wrist-snap" is taught to high level players as I've personally witnessed. I've seen, for example, Raonic's coach showing him wrist snap in practice. Raonic's serve, imo, doesn't really use much wrist snap, but I'm sure the wrist (meaning forearm muscles) are very active just prior and at contact, just to hold onto the racket if nothing else.
It seems to me that the best servers, are actually slowing the upper arm just prior to contact and this is driving a great amount of the force into internal shoulder rotation and pronation and forearm strength is necessary to deliver this power to the ball.