I thought the suddenness of the travel in the transporter and the flash of light were meant to suggest that the AI handwaved it all.

Possibly. But at what point did she stop? The transporter was supposed to take Woolsey from wherever the mess was to wherever his own quarters were, so if the AI handwaved it and only made Woolsey think he'd gone for a transporter ride, sooner or later Woolsey would have noticed that he wasn't where he thought he was on Atlantis.

I think it was actually Mallozzi who was handwaving it all.