You probably mean Medicaid, unless you're on dialysis or an extreme non-trad.
And no. My understanding is that graduate students don't qualify just because they have no income.
I'm pretty sure grad students don't qualify. Usually your schools plan is the best value, and (at least at my school) you can get one that'll cover your family. In any case it's bound to be better than Medicaid.
Some people with kids have medicaid, I think -- at least that's something I've heard here. Without kids, you don't qualify.
Your school will probably offer a policy, and AMSA has one as well.
Yeah she's right on both counts. Oklahoma has something called SoonerCare, the state's Medicaid program, which AFAIK is only for children. Actually their coverage is good enough for some mothers to quit their jobs in an effort to drop family income low enough to qualify for it.