I can't be sure by reading the rules, kind of a gray area.
Say your putt comes to rest supported by the cage of the basket, on the outside, but is ALSO supported by a tree. Likely without that tree it would fall (but you can't move the basket or the tree to find out)* this part may be irrelevant. Is it in?
Hole #4 at Lakeshore has the basket placed an inch from a large, split fallen tree. I have done that, it was technically supported by the basket, but also by the tree and definitely would have fallen to the ground if not for the tree.