Rules Reference, page 10, Enemy Engagement.
Each enemy in an investigator’s threat area is considered to be at the same location as that investigator, and should the investigator move, the enemy remains engaged and moves to the new location simultaneously with the investigator.
Thanks for this. I actually re-read this exact section, but I somehow still didn't understand this beyond the OPs general feeling.
Spoiler (click to reveal)
Still worth doing to get the croc out of the bayou.