If you can't do that then there will be a lot of people who are going to start popping up saying that they didn't get their money.
I'm not convinced that this is a drastically different scenario to what we already have in Bitcoin.
Alice pays Bob.
Bob denies receiving payment.
Alice publishes a transaction hash which anyone can look up.
Bob denies the receiving address in that transaction belongs to him.
If Alice is really lucky, she has some correspondence from Bob with the address in it which can be independently verified and which Bob cannot deny. On the other hand, there is a good chance the address was a one time address generated by a payment processor on a website and she therefore has no independently verifiable record of the address.