It is possible for something in the public domain to be ... patented.
IANAL, but I believe you're wrong on this one. Works in the ublic domain count as "prior art" and demonstrably publishing a work (where "work" is fuzzy, because for the most cases copyrightable works aren't patentable anyway, software in the U.S. being one notable exception) into the public domain prevent them from being patented by anyone else. A friend of mine used to work for a large manufacturing company in Germany and his job consisted of reviewing patentable works which someone else had already decided weren't worth patenting to see whether they were worth publishing so noone else could patent them. All your other points about copyright etc. are valid AFAIK.