HR departments generally have no authority over individual claims. Rather they work with insurers and independent employee benefits consultants to construct a health plan with certain benefits and coverage rules which they think will minimize costs (based on predictive analytics) without hurting employee retention too much. Large insurers offer employers a menu of options with various provider networks (narrow versus wide), negotiated rates, deductible / co-insurance / co-payment amounts, carve outs, special extra benefits, etc. Once the plan rules are set at the beginning of the year, the insurer just enforces the rules as written and passes the claim charges on to the employer.
Of course, sometimes health plans just make errors in claim processing and deny a claim that should have been approved. Or the provider makes an error and submits a claim with incorrect codes or lacking the necessary documentation to establish medical necessity as per coverage rules. Or there are gray areas where it's not always clear whether a certain service should be covered or not, and it comes down to a judgment call by a nurse or doctor employed by the insurer (medicine is still more art than science and the best treatment plan isn't always clear). This can be a huge hassle for patients dealing with serious medical conditions.
