Health Net claim denial "No authorization on claim"

After learning that a close relative was a carrier for a genetic condition, I received genetic counseling in-network earlier this year. At the time, I was careful to ask my provider what the cost would be to me, and I was informed that the standard battery of tests would be covered (minus copays), but that I needed an additional test that I would have to pay a few hundred dollars out-of-pocket for.

I received the genetic screening and paid all of my bills and copays on time. However, earlier today I received a letter from Health Net stating that a claim for ~$9000 from earlier this year had been denied due to “(4625) No authorization on claim—resubmit with auth.”

I moved in the interim, so I don’t think I received all of the correspondence leading up to this. It looks like there’s a way for me to receive copies of information relevant to my claim from Health Net, so my next step is to do that. However, I’m still struggling to wrap my head around a few basic questions:

Whose problem is this? If Health Net denied this claim, am I liable for the $9000?

Looking more closely at my summary of benefits, it looks like genetic testing is not covered unless the provider obtains prior authorization. Does the denial mean my provider failed to obtain prior authorization? Was it my responsibility to realize that they would need prior authorization, or was it up to them?

Do I need to call my provider to tell them, e.g., that they should be resubmitting with authorization?

If I am liable, what should I be looking at doing (e.g., filing an appeal)? Where can I go to get more information to try to protect myself a little bit?

Obviously, I’m pretty freaked out that I might be on the hook for $9000 that I did not expect to pay and did not realize I would even possibly need to pay. But these things are so impossibly convoluted, I still have no idea if I’m even really a party to what’s going on, or if it’s between the provider and Health Net.