I understand the logic completely. The phone could be "accidently" wiped by the police. I can't say that all the potential information is saved by the billing system.
Can't you? You ever get a cell phone bill? They usually read like telephone books, nary a call made, even if its for 1 second, is omitted.
What is stored locally would be a phone directory and the actual text messages, perhaps, but that would be erased only if the "hard drive" was removed, I believe, not a "dead battery"