I just pay a health center fee along with my tuition, it's $30 per semester.
I don't know how your school does it, but where I did my undergrad we had the health center fee that covered the operations of the health center, however we were still required to carry insurance as well. The school where I am currently doing my PhD has the same policy as well; the two are located some 1,000 miles apart.
It may be very different other places, but most colleges? That surprises me.
I am not aware of any colleges that don't, at the very least, require hospitalization insurance for students. If a student attending that school were to be injured on the grounds, the school could be liable for the cost of the student's hospitalization if the student carried no insurance, even if the injury was of no fault the school.
About 20 percent of college students aged 18 through 23 (1.7 million) were uninsured in 2006
Source: Education Resources Information Center
I'm insured, but my college has no process to verify that. We're a community college in New York.