I have thought for a while that the phone explanation from LE made little sense. It may be the type of phone that doesn't ping when turned off, but when did it turn off? And where? There appears to be a cell phone tower on Landry, right behind the LCG building (this is from google map, please locals correct me if this is wrong). If she went missing at or around this point (I have my doubts) and the perp or the accident turned her phone off, they should be able to track when and where her phone turned off (approximately, if the phone is not equipped with gps, it won't be exact bc it will be triangulation between towers).
Saying that she has the "type of phone that doesn't ping after it's shut off" sounds like good info, but really it's vague and not informative at all. I really, really think LE has specific info regarding the phone.
One other thing - I think it is unlikely that her phone's battery died naturally. I do believe it was purposely turned off or damaged in the incident. This is based on two pieces of info: 1) When Brettly's phone died in the middle of a conversation with a friend, that friend called Mickey's phone. If her phone were about to die too, I think she would have mentioned this. Something along the lines of, "yeah, sorry the call wasn't dropped, his phone died. Mine's about to die too..." and 2) her sister was very clear about the fact that they shared the same type of phone and the phone has a long battery life.