How easy is it to submit a claim to have your HSA pay? It says I should wait for explanation of benefits, then submit the payment - can I do that with the HSA debit card? Is there some paperwork involved if you can't do it through the debit card?
If you do consider going the HSA route, I would strongly urge you to NOT submit claims to have your HSA pay. You'd be missing out on some of the best HSA advantages.
Suppose you go to the doctor and get a $100 bill. And suppose in 40 years time you have a $1500 medical bill for a colonoscopy. You could use your HSA to pay that $100 bill directly (with a debit card or with checks depending on your HSA provider), or to reimburse you if you chose to pay with a different method. But that wouldn't be the wisest move. You still have that looming $1500 bill coming in your future. Sure you'll have $100 more right now. But in 40 years you'll have nothing and will have to fork over that $1500.00. Plus, you'll be that much closer to probably having to pay ~$3 in HSA fees every month for having a low HSA balance (the whole point of this thread).
Instead, you could invest that $100 within your HSA. In the next 40 years, it would be worth on average $1631.14. If you use that $1631 for medical expenses (and who doesn't have medical expenses when they age), it is fully tax free. Assuming a 25% federal and 7% state tax bracket, that saves you $521.96 in taxes ($32 on the $100 you put in the HSA and $489.96 saved on the earnings). That colonoscopy would be covered without you putting in another dime.
You lose $100 now, but you gain a free $1500 coloscopy in the future, save $1440 on HSA fees by avoiding a likely $3/month low HSA balance fee for those 40 years, and save $489.96 on taxes over that 20 years. And you'll still have $131.14 left over to withdraw any time you wish.
All that for a $100 doctor fee. Now imagine the gains and savings by putting $6500 in it each year and not reimbursing yourself from it. Hint: You'll have $1,482,758 in 40 years assuming you get a typical 7% return on your investments.
There just is no better legal way of saving money at the moment in the US than to leave as much money as you can in the HSA and then invest that into stocks. So don't reimburse yourself from your HSA for medical expenses. Think of it as the single best retirement plan possible, combined with decent but not great health insurance.