Is It an Intruder?

The intruder theory only works if the letter was written before the attempted abduction of this girl. And that there was no really true intention to ever return her. The parents don't know that she's dead. Even, and even if they were, even the sentence of denied a proper burial indicates that the author of the letter understands that even the return of a dead body has some value. If you don't solve this thing in the first 48, you don't have a suspect in the first 72. Time is the killer.