Yep, Paul, same stuff. 3' x 5' sheet, 1/4" thick is what I use. Here's a picture of what's left of the base of the Shade Gap station, after being outside for 5 years (it deteriorates to this point in around 3, I just haven't had occasion to remove the station until this summer.)
You can see the squares still on what's left of the top layer, a distinct middle layer, and the bottom layer. (The majority of the top layer stuck with the walls of the depot when I lifted it up.) None of these layers have much of any strength left at this point, breaking with minimal effort.
I saw the same display with the board in the water, which is why I researched it and ultimately chose the stuff for this purpose. I figured if it could stay in constant contact with moisture, then it'd be perfect for building bases. My guess is that since neither of you guys appear to be having issues, it's got to be a freeze/thaw cycle thing since I'm in a decidedly colder climate than either of you. I bought multiple sheets at different times at different stores for various projects, so it's not just a "bad batch" issue.
There's a different tile backer board I used for the walls of my buildings, called Fiberock. It's a US Gypsum product. It had the distinct advantage of being able to be cut with a regular saw, which is why I chose it over the HardiBacker for the walls of the buildings. It, too, hasn't held up to the elements (despite my two-winter "trial" with a skeleton station sitting outdoors which gave the impression that it would survive. Evidently, 3 - 4 years is about its life span in that environment.) It doesn't delaminate like the HardieBacker, it just loses its strength and disintegrates if handled.
So I'm back to using GatorPlast or 1/2" blue foam, as they seem to hold up the best to the elements out here.