Personally, I like how that engineering turbolift transforms into Jefferies tube access sometime around season 4?
Well, we know Crusher arrived through those portside doors to set Q's back in "Deja Q", but we didn't get to see what was behind those doors. Perhaps Crusher was in the Jeffries tubes at the time the alarm was sounded, trying to disentangle Ensigns Lusty and Smolder or something, and climbing down a few decks was faster than crawling out and getting a 'lift?
It would make sense for Picard to decree that all medical emergencies pertaining to Q be handled by the CMO and the CMO alone... No matter where she happened to be.
Timo Saloniemi