The guy wanting to marry her explained that his company took over the SAO servers once Argus or whatever company went bankrupt. I would imagine with enough documentation and tinkering, not only could he have prevented her from actually logging out, but also transferred her to another game/server. I'd also suspect this would allow him to muddle her memories, but since I haven't read up on the LN and the next episode hasn't aired, I dunno how much of her is actually intact.
If it makes it any easier, just think of the brain as an organic computer that this tech is capable of manipulating as if your personality/memories were software. Since it was mentioned there 300 others still in a coma, I'd bet he couldn't isolate just her info and probably just wound up transferring a chunk of other users to the new game.