.. The operator could easily invest their own money into the ponzi from various addresses, knowing that they would have the money returned to them even if they have to payout to other investors. If they do not receive enough money then they simply run away with their own money plus the money of their other investors.

The idea with ponzi games is that the operator does not play. Its PvP players gamble against each other and the operator gets a little bonus for providing the service. Youd have to prove this for a ponzi to be provably fair. So you have to prove that a certain person and their friends are not playing. Proving a negative is considered impossible.

tl;dr: A provably fair ponzi would have to prove either that the operators are not playing or make sure that everyone is a player.....