I’d say your position holds even if someone is a moral realist because the problem of the criterion shows us that we cannot be certain about moral facts, just as we cannot be certain about any facts. To claim otherwise is to suppose unjustifiable special ability to know the truth, which is a position some people take but which, for anyone other than themselves, does nothing to resolve uncertainty.
I’d say your position holds even if someone is a moral realist because the problem of the criterion shows us that we cannot be certain about moral facts, just as we cannot be certain about any facts. To claim otherwise is to suppose unjustifiable special ability to know the truth, which is a position some people take but which, for anyone other than themselves, does nothing to resolve uncertainty.