StructuralEIT,
The philosophy that you are talking about can be reasonably applied to a W section as the majority of the section is in the flanges.
In this case, more than half of the tube area and a significant amount of the section modulus is in the walls, and should not be ignored.
Personally I would check the welds under a triangular stress distribution.
But at the very least, if you are going to assume that the welds to the flanges are taking all the bending stress, then you need to check that the flanges can take this stress on their own.
csd