Maybe these weren’t doggies, but coyotes or wolves?
It makes sense that native dogs would flow over to Jamestown. Straying dogs will try to set up a relationship with any humans they meet.
For instance, the native Tasmanian's never had dogs but when the English arrived, a few of their dogs strayed over to the Tasmanian settlements and set up a relationship with them.
Bagged a yote one fall. Took the precaution skinned him out. I’ll be danged if those hams didn’t look good.