I would go a little purple in those cold conditions too.
Colder conditions can make a difference to colour, so can soil.
Being on the south-eastern side of a tree it would get first sun of the day which would help. The other plants could help keep the ground from getting too wet and provide protection to the base of the plant. Any leaves covering it over winter will also help. It's a micro climate, but still quite unusual for it to survive.
It seems to fit, unless there's another basil like it but that seems doubtful.
