"Posting something on the internet does not make it public domain."

This is where I find your point to fall apart. The internet is NOT under the laws of any given nation and I doubt very much if some nations even have a sense of Public Domain or copyright. And even the ones that do can hardly agree on common terms.

So really your statement should be "Posting something on the internet does not make it public domain in certain jurisdictions if covered by applicable copyright laws"

And that is why it is stupid to expect something you post on the internet to not ever be copied without your permission.