Dispute "non-covered service" denial?

My wife and I have been trying to conceive and I went to my Dr with infertility concerns. After discussing with them, they ordered labs to help evaluate it: some blood work and a semen analysis. All in all, 5 items showed up in my claim (3 related to the blood work, 1 for the semen analysis, and 1 for the primary care visit). My insurance covered the PCP visit, but denied all the rest with code PS0: Non-covered service.

Except, I'm pretty sure it is covered? Here is the relevant section from my plan documentation. As a layperson, it sure seems like "services or supplies for the evaluation of infertility."

So, is there a proper way to appeal this? It seems unlikely my plan doesn't know what is covered, so maybe it's a documentation issue? Although that's not what they denial says. Maybe it was coded incorrectly?

Ultimately, if I'm unsuccessful in getting it covered, can I ask the hospital to reduce the amount to the in-network rate? It seems like I'm currently being charged the unadjusted amount.

submitted by /u/rvH3Ah8zFtRX