That is true for the stocks but not options. Anyone with a brokerage account can write some calls and if they get exercised it’s up to them to find the stock to buy. Most pricing models assume the liquidity is always available but that’s not necessarily the case.

true, but the other side of that trade is almost always an options market maker who will hedge their delta by trading the underlying stock. so, yes, buying a call doesn't directly represent share ownership, but it almost always results in a commensurate share purchase. not 1:1, but reflecting the delta of the option.