Yes, that occurred to me, but it doesn't necessarily support the claim that she wasn't raped, just that she wanted to get out of a trip to the drunk tank, even though she probably came up with the rape claim to get out of being committed, which was something I suggested way, way back when this case first broke. It might show she was trying to come up with something to prevent being taken into custody, but once she was in custody, it would no longer have a direct influence in claiming that she was raped.
Yes, it could explain the police call about checking on the kids, but not why CGM wanted a man she didn't know well to pick up her kids.
Unless she actually did know him well...., which is what I am leaning toward.