We’ve always had to provide proof that the child WAS covered under our policy, lifetime maximum, deductible, and out-of-pocket max. The lifetime maximum had to be high enough and deductible low enough. We never had to provide any premium or co-pay information. Our policy greatly exceeded the one they offered and we filed our paperwork early so we always were able to opt out, except the year our S was aging out of our policy so we bought theirs.
The policy our kids’ U offered was decent, but our policy allowed them to get coverage in our state for both kids to see the docs they had been seeing for years. It also allowed them to go to any provider (better when participating & preferred) and have some coverage, without any referrals. We were happy not to pay premiums for them to have EXTRA health insurance.
The premium is none of their business, so I would say that and decline to provide it. HSA/HRA is also none of their business.