Brick Pimiento ending his introduction to the show with "and there's definitely no ghost" is initially passed off as a poorly attempted coverup played for goofy cartoon humor. He meant for it to be taken as a desperate attempt to hide the scary goings-on, either to use the incident for publicity or so no one would realize that he was one of the Phantoms (depending when he first donned the mask).
Brick being especially nasty to Chrissy during the show (by telling her that her dad's been arrested) could easily come off as him losing his patience with her constant attitude. However, with the reveal that he feels incredibly insecure next to the talent stars, it's possible that her calling him "doofus" pushed a button.
Fred's assertion that everyone must run into ghosts and monsters all the time might seem a bit naive, until you consider that in the world they inhabit, he might not be wrong, given the sheer number of mystery solving teams that Hanna-Barbera has created over the years.
Why isn't Steve Trilby, the original Phantom, arrested for his past crimes? His crimes were committed in the 70s; most likely the statute of limitations ran out on them.
Granted, Daphne has probably heard jokes like the ones she uses to throw the contest before, but why does she use the same ones that Shaggy and Scooby used to try to impress Brick Pimiento? They probably told the rest of the gang those ones recently, leaving them on her mind when she needed them.
With a hefty dose of Squick, one realizes that when Scooby and the gang first see the Phantom, he is "menacing" Chrissy, which they observe on a security camera. Except that Chrissy is in her dressing room. There are security cameras in the dressing rooms, and two of the contestants are pre-teen girls.
