My tax return shows a full year exemption for health care, form 8965. I did not request this, do I really qualify for it?

If you are claimed as a dependent or your income is low enough you are granted an automatic exemption.

Look here to see what your exemption code is for ... if you still think you don't deserve it you can amend the return ... https://www.irs.gov/pub/irs-pdf/i8965.pdf