Harvey, that's an interesting question.  My experience of tree wells is that they are a steep bowl with the bottom at the tree, or with a space that has been filled with spindrift...so that it LOOKS like it is a snow surface, but is a spindrift trap.  The surface is a steep slope down, filled with drift, if there is anything there at all.  The drift, sort of like skiing in fresh powder, takes on the properties of a fluid rather than a solid.  Push on it, and there is no purchase, and this is why it is so hard to get out.
The Mammoth situation was quite different, where the steam created a underlying melt...somewhat what can happen with a stream and a snow bridge.  It created a void under the surface that progressively lost strength, then gave way.  They fell into a clear space.
As I understand it, quite different mechanisms.