There has never been a definition of what constitutes owning the residence, I mean is it just living in it, can Willow or Tara invite vampires into Buffy's house in Season 6 since they were living there. Xander and Anya couldn't in Season 5 Real Me, only Buffy, Joyce or Dawn could.
Is it possession of keys or a legal document?- unlikely because why would that affect a vampire.
I think living in it for more than a certain amount of time would be the most reasonable idea. 24 hours maybe, Faith was in the appartment at least 3 days probably more like 4-5.
Cordy: "On Monday, - a guy was beaten up here, his wallet and car were stolen. He's still in the hospital. Four blocks over - is a restaurant where they had a major knock down drag out on Tuesday. Then here another guy ran into something he referred to as 'the bitch from hell,' who sent him home with paramedics. - That was on Wednesday."
So if we go by duration then Faith could invite someone in and since we know that a vampire can be preinvited (from Cordelia's preinvite to Angel in Rm W/A Vu) then this quote takes affect
Faith: "You think? Because what if you kill me - and you experience that one true moment of pleasure? Oops! I'd get off on that. Go ahead. Do me. Let's take that hell ride together. Come on, Angel, I'm all yours! I'm giving you an open invitation.
So I think that can be used to explain it