Now, if there was proof of them having the same IP as each other on other
occasions, or the two identities overlapping in one session...?

Indeed, the sequence posted elsewhere in this thread has the IP address
returned to the original poster within minutes. (See Message-ID:
below).

This has also happened at least twice. A quick back of the envelope
calculation shows the chances are not a million miles from a trillion to one
that the same ISP connection wasn't used to send messages from both posters.

Christian.