Yes, I think you are basically right. Put call parity is essentially model free, at least in terms of not relying on any assumptions about the underlying asset price dynamics. The canonical reference here is Merton's paper (Theory of rational option pricing). Buying a call and selling a put with the same strike price and expiry is tantamount to making a commitment to buying the asset at the strike price. That is very similar to a forward contract, with the possible exception that a standard forward contract is struck at a price that makes the initial value equal to zero. So, what can go wrong? I suppose counterparty performance risk. Or borrowing and lending rates being very different. Or shorting the underlying asset being impossible, or at least costly. But, given that the relevant trading strategies only call for establishing a position once and then closing it out at expiry, the supporting assumptions are not remotely as stringent as those underpinning the Black Scholes model.