I have an Emacs running, and a middle-click pastes text that is not
the primary selection (note: it is not the content of the clipboard
either, as seen with Ctrl-Y). Changing the primary selection by
selecting something else in an xterm does not solve this issue.
Running a different Emacs instance does not show this issue, thus
the bug is in Emacs and is visible under some unknown conditions.

I could eventually avoid the issue without restarting Emacs by
selecting some text in the running Emacs.