Got a good look, if it was painted it was an amazing job. (PS: it was exactly that.) See added photos. As mentioned, it's not the first I've seen (completely different places).
Yes, I think there may have been a ring, that's definitely a clue I should have been paying more attention to. Too distracted by the fabulous paint job!
Seriously though, I suspect a genetic quirk. Pigeons do have unusual variations due to the human selection in their history. You sometimes see ones with feathered feet for that reason. Like dogs, basically.
PS: looks like your theory is correct. The invisible hand turns out to be very human. I'm impressed.

