And your very statement - "does not accurately reflect reality" - implies that reality can be accurately reflected, for how else would you know that someone had not accurately perceived reality?
You're right, I'm totally taking it on faith that objective reality exists. Perfect accuracy does not have to be possible in order for it to be true that some perceptions are more accurate than others.
How do you know they are straight? I say that they are curved. Now, show me I have judged incorrectly, without affirming that I have the ability to judge.
Take a ruler. Multiple people observe the ruler under various conditions. Very nearly all people agree that the ruler appears straight in almost all circumstances. Multiple people place the ruler next to the line and agree that the edge of the ruler and the line are a similar shape. The majority of observations that the ruler appears straight are more likely to be relatively accurate than the contradictory observation that the line appears curved. Probability can be calculated mechanically.
Perceived judgment is the same as perceived choice, or any other aspect of apparent free will. It doesn't eliminate the possibility of illusion. My point was not to argue which state is more likely, only to maintain that determinism is a logical possibility by correcting a misunderstanding about what an illusion is.
the very concept of "illusion" implies that I had a choice
No, illusion is when perception does not accurately reflect reality. It does not imply choice. Take the Hering Illusion for example. The red lines appear to be curved even though they are actually straight. We don't choose to see the lines one way or the other. That's just the way we see them.
Of course it's obvious that we have free will. We make hundreds of choices every day. But the fact that free will is obvious does not eliminate the possibility that it could be an illusion.
"The one charm of marriage is that it makes a life of deception a neccessity." - Oscar Wilde