Thank you to everyone chimed in. This gives us a fair bit of information to work with. I still suspect that this doesn't happen on edits, and that it's just a few people gaming the forum functionality to avoid the "edited" footer. Rama's description matches Tom's behaviour - he edits posts, deletes and reposts, edits, deletes and reposts, etc. If you catch him in the middle of that cycle, everything adds up.
Nonetheless, we now know what is claimed and we can see if we can reproduce it. If we can't, we can still ban the behaviour described above (both because it's shitty and because it'll help us rule that option out).
I'm very sorry I haven't done anything about the 2 feature requests currently active in S&C. Today is the last day of term at work, so after a quick recovery period this weekend, I should have a bit more time to do some investigatin'