It shouldn't say "Accepted Solution" - that got my hopes up that there was going to be a way to do it.
So, how am I supposed to find out what the appearance is set to so that I can make the other pieces in the assembly look the same (as whatever the heck this bozo from ten years ago used for just this one piece for whatever reason)?
[I think I might have an answer - and it might even be a better solution: I'll open up the Bill of Materials in the Assembly and then I can add the Appearance Column and Copy and Paste them all at once! I can stretch that column, but doesn't anyone think that it is foolish to have that tiny little window and then go and give the appearances names like this:

You can kind of tell if it is one of the first four vs. the next five vs. the next pair of Stainless appearances, but how are you supposed to see what it is before you go picking one from the dropdown?
I wish I knew what sort of workflow these guys had in mind when they go and make decisions like, "Duhh, let's make that window so small that you can't hardly see anything in it!" I'm surprised that they didn't go, "Let's make the appearance window 5 characters wide and make all the appearance names start with "Color"!"