Should I appeal denied claims that I have 0 responsibility?

Hello everyone. I wrote a case a couple of months ago about this case. I have Anthem PPO in California.

To make a long story short, I had two hospitalizations this year, one for an infection after a surgery and another 2 months later for colitis/gastroenteritis that was not directly related to the surgery but it is possible that the antibiotic treatment for the first infection made me susceptible to the second infection. For second time the doctors told me a couple of times I didn’t need hospitalization but later I was admitted for a day and a half because my high fever. Blood cultures results that came after I left the hospital showed that they found the Campylobacter bacteria on the blood.

Anthem denied 2 of the hospitalization stays, one for the first infection and one for the second (for the first infection I was treated in two hospitals and they approved the claims of one of them. I know that the first hospital has sent the medical information to Anthem, around a month ago.)

Both times the claims were denied but showing that I had 0 responsibility in the EOB. One of Anthem representatives told me that if the hospital cannot show the medical necessity, they had to write off it. But another told me that they could charge me, after I asked why my HSA account show the claim for the amount of the hospitalization.

My big question is, since I have 0 responsibility, should leave them like that and leave it to hospital and Anthem? Or if I don’t appeal is it going to come back to bite me, with a bill from the providers?