There are many things that are too small, too large, too fast or too slow etc. for us to notice. For example, you miss out all the air eddies you create as you move through the atmosphere. Lots of things are also simply out of sight and our minds construct perhaps 50% of what we perceive by pattern completion. I think what we perceive is mostly right, but in many ways it only corresponds superficially to the computations that are actually going on.
I don't find this distinction very useful either though. Yes, there is an illusion of confidence in the accuracy of what we experience, and a lot of it is tainted by values and false memories, but still, it seems plausible that our experiences correspond very directly to things happening in the universe.
I also don't agree with the claim that mathematics being real in a Platonic sense is an illusion. It all comes down to how you define 'real'. I find a sensible definition is that it is a thought that corresponds to how the world works, to things in the world (future, present or past), but also to how the world hypothetically, but very plausibly works. In the same way as you can plausibly assume that any imaginable thought corresponds to something in a remote region of an infinite universe (or multiverse), you can also assume that our mathematical theorems correspond to some computation somewhere. It makes sense to extend the definition of real by immediacy: The fictitious novel is also real (in some multiverse), but it does not have as much immediate real-ness as mathematics. For mathematics you can find all kinds of correspondences in nature (e.g. 1+1=2), but in the novel you can mostly only find things you've previously taken from nature to write the novel, but if your predictions are very real, then it might at some point be impossible to tell whether it is true or not (just like a computer game that almost looks real).