I bet LE has talked to his ex GF. I bet she had info
I have been wondering about this as well. From the below article from a few days ago: (this quote from his grandmother) "He had a live-in girlfriend but I dont know what happened. They lived together at his apartment."
http://hollywoodlife.com/2014/09/22/hannah-graham-person-of-interest-identified-jesse-matthew/
I'm unsure whether she meant they lived together currently or not.