Therapist should have blurted out where Martin was found.
If she tells the detective where Martin was found, or at least that he got pushed off a dam, before she could possibly know it would corroborate at least Liz's final murder confession.
Though perhaps we're not supposed to think that Liz told the story in as much detail as was shown, but that's kind of bleh movie making.
http://www.imdb.com/mymovies/list?l=32504872