I deal with fat tires pretty often now, I would say it's usually up to pot luck. It's almost a hard fair bet that the big tire will not fit up on a small rim. I've tried putting 4 inch wide tires from a 26 rim to a 27.5 3 inch wide rim, definitely not a match.
They usually work well when using the same sized rim just different width. Ive send 26 3in wide put with success onto a normal 26 rim. Works great I'll add, and they guy ain't small neither, just gives it a more puffy appearance.
A 26 diameter with 4 inch tires is closer to 34 inches total diameter, they are visibly taller standing than the standard 26. About as big as a 27.5 with 3inchers.
The best way to judge is the width of the frame in the area where the tire will be, if it's wider than the tire is meant to be, then it's fine.