Aha!
I followed Doug's suggestion and found that an all white image becomes 252,254,254 when doing the conversion step with the Adobe CMM conversion engine, but it's 255,255,255 using the Adobe (ACE) conversion engine. So, is it safe to assume that Photoshop must be using the Adobe CMM conversion engine when printing?
OK, so then I checked my Color Settings in Photoshop, and the default conversion engine is set to Adobe (ACE). Hmm. Not what I expected, since if that were used when printing presumably this problem wouldn't happen.
Now that it seems to be it might be Photoshop-related, I'll admit that I'm way back on CS 5, if it matters, and I don't have an option to select which engine to use in the print dialog. I think I'll just update to CC and see what happens...
Bob: I'll check out Mirage.