You should be a forensic plumber, because just explained the enigma!
Thinking more about what you so astutely observed, I can see that someone probably *glued* the tailpipe (upside down, with the hat on the bottom instead of on the top!) into the sink basket.
No wonder I had trouble unscrewing the cast aluminum retaining ring!
They *glued* the sink basket into place, from the underside of the sink!
It hadn't occurred to me until you mentioned the glue, but I just realized there was no plumbers putty to scrape off in the sink!
My sister tells me the Sears guy who installed the Kenmore reverse osmosis water filter had last removed and re-installed the pipes, so, I suspect (without any more evidence) he was our lazy culprit!