You're wrong. I'm at a UC at the moment, and much of the funding is determined by the state's budget. The state has recently made HUGE budget cuts to the school system, which has caused tons of cutbacks, including less funding for graduate students. My school was supposed to accept a much larger number of students with TAships this year, but they were unable to due to funding.
Anyways, I got back from visiting UIC yesterday, and I was super impressed. I had never been to Chicago before, and despite being as cold as everyone says it is, the city is really awesome. It was much cleaner than I expected it to be. I met with two of the mathematics staff, and also with a few grad students from the mathematics, statistics, and computer science department, and everyone seemed very welcoming. It seems like UIC has a strong department that also seems rather informal and personal. Both of the staff members also knew a couple of the staff at my current university, so that was cool too.
I would highly recommend checking it out if you were accepted, and to those of you planning to attend, I look forward to meeting you in the fall.
As far as funding goes (at UIC), I talked with Kari Dueball (the person who handles it all), and she confirmed that funding is pretty much guaranteed for the length of your degree pending no unsatisfactory behavior. She also said that summer TAships are kind of limited, but that most of the people who want one get one. It seemed to me like the only people who ever got excluded from that were 1st and 2nd year graduate students, as allocation of summer TAships is done via seniority. She essentially said that the school understands that the department's grad students support a large number of students from a variety of departments (it's math, everyone needs that), and so funding is found to support them. This is very different from the school I'm at now, and was very impressive to me.