Not clear on whether someone who receives "funding" necessarily has to follow federal guidelines, but this issue is neither here nor there in your situation.
If you're saying that they knew you were HIV simply due to the name of your doctor or you believe they investigated it before submitting your health insurance paperwork, I'll allow it's possible.
This could go either way, but I'm leaning toward suspicious. I'd contact the EEOC and advise that you believe you were fired because of your HIV/disability status and the reasons they gave you were too coincidental for your taste and you believe them to be pretexts.
"Should I persue something, especially on that medical benefits thing."
Not exactly sure what you mean by "that medical benefits thing", but if they never submitted your health insurance paperwork in the first place and you were never enrolled, technically COBRA doesn't apply. But given the givens here, I suspect the EEOC may address this as well (or refer you to the Department of Labor on the COBRA issue).
Or EEOC may just issue a right to sue letter, in which case you need to be interviewing discrimination attorneys at some point -- you'd have to sue within 60 days after getting the letter, but that may be months down the road. I believe there are punitive damages available under the ADA statute for violations, as well as compensatory damages.