Claim denied. Hospital sending to collections. Do I have any rights?

I moved to the US from Europe, I thought I overall got a hang of the US insurance system, but just got very confused again.

Can someone explain me the different cases where out of network benefits play a role?

I thought whenever a provider is not “in network” with your insurance or does not take your specific insurance plan (like, they take an BCBS HMO plan but no BCBS POS plan) one can use out of network benefits to still get the service covered, usually with higher deductible, copay, coinsurance and a higher and separate out of pocket max. Now, I reached out to a provider about continuation of care when relocating to a new workplace, different state, different insurance company the employer offers health insurance with. They said to make sure I have out of network coverage because

“out of network benefit is required to see a physician/facility for hospital outside the state”.

So is out of network based on geographic location? Or on the doctor’s insurance contracts? Or both?!?

Add-on question: That specific provider is not in network with any insurance, currently I have a network gap exception. So it’s covered with my in network benefits. When moving to a different state, will that not be possible and I need to pay the higher costs I have with the out of network benefits, even if a) it’s continuing care and b) it’s specializes care, not impossible but hard to find elsewhere?