That statement is logically incorrect.
It's actually mostly correct - which is my entire point. Few things are so black & white.
They already state why incorrectness matters
Limitations and assumptions do matter of course, but misleading usage of the term "incorrect" is the issue I'm referring to. Unless if by "incorrectness" you mean "the degree to which this differs from perfectly correct in all cases", in which case you could maybe try out the term "accuracy" instead.
To the contrary, it is more often a valid, scientific reason for rejecting the model in question.
I still feel you're arguing about something I'm not. To restate, declaring something to be "incorrect" because it's not 100% perfect in every way is not a valid, scientific reason to reject a model.
a universal problem with climate modelling is the lack of empirical testing of these models
Well, except their predictions are empirically tested against new observations constantly. Of course no scientist expects them to match perfectly, since they are of course simply approximations that make well-understood assumptions like "short-term weather and cyclical patterns such as ENSO and PDO by their nature do not affect long-term trends". That does not make them useless for predicting long-term trends, which is why said empirical testing usually leads to further refinement instead of rejection due to not being 100% perfectly correct.
You may even find that actual, practising climatologists understand the limitations of their own models far better than you do. So you may have to come up with a more accurate reason than "your models are incorrect because you don't test them empirically" to be convincing.