Since I asked that question, I have heard from friends who used my CHAdeMO adapter a few times before theirs arrived. They found that my adapter worked best when connected to their car first. Their adapter works best connected to the CHAdeMO cable first, as TaoJones does, which I think is the standard procedure. That suggests to me that not all adapters behave identically, which seems odd. But all that matters to me is that it does work! I have found it extremely useful when wandering off the supercharger network, although Tesla is about to make it unnecessary on US 101.
I've found that some Chademo stations behave differently than others. Even ones of the same type in the same networked. Basically, chademo is not a particularly well designed connector and can be finicky.