Insurance company has nothing to do with it.
If you have a qualifying health insurance plan and no non-qualifying plans, then you can contribute an hsa anywhere you want.
Generally, you’ll want to have the deductions come right out of your paycheck if possible, due to more favorable tax status, and that might mean opening an hsa at the employers preferred location.
If you can choose, Fidelity is the best option though by far.
Have you seen: If you save and do not spend your HSA, how/when do you plan to use those funds?