ETFs are not like banks.
For example, BlackRock will buy X amount of bitcoin and give it to their custodian (Coinbase) which will then give BlackRock a receipt which is what goes into the ETF.
Coinbase or any other custodian would be the one that could fuck around and create paper bitcoin, but I’d imagine BlackRock and the other institutions will be looking at the addresses to make sure the Bitcoin they have a receipt for is there.
This is my understanding anyway. The whole ETF = paper bitcoin meme comes from a lack of understanding it seems. Fred Krueger commented on that on a recent video