That fixed the problem. I had Torbutton installed, but never really used it so it was no trouble to disable it. Now, after repeated testing, CCleaner is wiping the cookies out as normal.
Why Tor would be doing this is mysterious. Tor is supposed to be the "anonymizer" for browsing, and here it is keeping cookies. Whatever, this CCleaner bug can be considered closed, or at least understood, can't expect the good guys at Piriform to accommodate the weird behavior of every add on.
Thanks a lot for your help QEM.