It seems that "exemption" (vyňatie) in this case means they were "exempted" from insurance retrospectively, i.e. their insurance coverage was terminated backdated because they provided false information or otherwise violated the policy rules.
So the coverage is rescinded, and they are liable to refund insurance payments made by insurance company to their service providers. That's when "pohľadávky za poskytnutú zdravotnú starostlivosť voči poistencovi" arise.
An unusual way to say that, I must admit.

here's the Slovak link giving more insight into this concept (third paragraph)
http://poistovne.sk/29399-sk/vszp-sa-vratila-cast-penazi-cez...

and English links (not exactly the same situation, but they give idea about retroactive termination).
https://www.healthcare.gov/glossary/rescission/
http://craford.com/blog/2016/3/21/cbxlayhmpeocdwxaiybvuy69er...