The forum's BTC on OG's keys is the forum's bitcoin, but the keys themselves are the property of OG and not theymos or the forum..
Yeah but most airdrops depended on the amount of BTC in that address, except maybe CLAM, but even that required a certain minimum. Og is entitled to sign a message with that address and to get 0 GBYTE for the 0 BTC he had in it.
Is an exchange a scam if they claim airdrops on their keys that are full of customer funds and not disperse these claimed values to the customer?
I would consider that quite shady, if not technically a scam (because they didn't promise me any airdrops).
Granted the only custodial account of any significance that I had at the time was with Coinbase and they did eventually credit BCH to my account. I don't know if they claimed GBYTE. I think that's very unlikely.