IMO, AxC intentionally misdirected police to buy time and CD followed his lead.
AxC did the same when police arrived after he’d shot CV. In the police body cam video, AxC was asked to spell the victim’s name and he spelled it “V-a-l-l-o” and said he didn’t know the victim’s DOB. Since CV’s wallet and phone were not onsite, but rather were with LV in CV’s rental car, all they had to go on as far as ID of the victim at that point was what AxC told them. So, presumably, when they looked up “Charles Vallo” from the info AxC gave them, they would not immediately hit on the recent reports by CV about LV emptying the house and locking CV out or CV petitioning for a mental health check of LV.
Once LV finally arrived back on scene, they’d have the info, but AxC’s first impulse seems to be to misdirect in such a way that he could later claim unintentional misdirection.