Edna was definitely wrong for not telling the parents...
At least than she could've stop the inferno that exploded by Amy's parents.

As for Tommy, well can't say for sure he's completely the man he says he is, but there is some honesty in there. The one thing I liked about him was that he did told Amy not to make this about him.
Here's a thought:
Doc. Abbott deals with many of the town's people, I'm really really sure he's good friends with some local police people. If he asks indirectly, I'm sure someone can tell a little bit of Tommy's past records (if any) especially since he worrying about her well being.
I've dealt with neighbors and coworkers that sure hell spill thebeans and the evidence to back it up...