The thing is, they don't just have the model sitting there looking pretty, they are using it to make sense of the world. It's like trying to detect a rootkit after it's been installed -- potentially very difficult because it can alter your whole view of things.

Here's another example, imagine that you are a creationist faced with fossil evidence for evolution. How do you deal with that? Maybe you think, "God must be testing my faith", after all, isn't that exactly what a meddling god would do? Now the fossils are proof of your meddling god! (who else could have staged such a clever test?)

The perception occurred accurately for the creationist, but then the opinions based on that perception had to be woven into a strange hypothesis in an attempt to circumvent the obvious contradiction between the fact (the perceived fossil) and the mental model of creationism in the perceiver's head.

A person has to be pretty far gone when they have automatized evading perceptual evidence to such a degree that they are no longer able to be consciously aware of the contradiction between their beliefs and what they perceive. This kind of evasion can be seen in cults, extreme religious groups, extreme political groups, where extreme = evading perceptual evidence that disproves your held beliefs. Usually group pressure is involved to automatize the evasion.

Perception (and I've been using it in the strictly integrated sensation sense) is our link to reality that enables us to make sure that our mental models don't fall off the deep end. Evade perception at your own peril.