This is very much a Dischurners sanctioned approach. On the Disney/FIRE thread our benevolent dictator (not sure if he's a dictator over there, but he did start the thread)
@SouthFayetteFan mentioned this very strategy. I've just switched over from using my HSA card directly for medical expenses, and its really easy to do in my HSA system - it is linked to my insurance, so it tracks what the bill was, how much was paid by insurance and how much is "unpaid" by the HSA. I can either have the HSA send money to the provider, or have it reimburse me. So we are now using credit cards for all our health expenses and then getting reimbursed by the HSA. You can do the same thing by just keeping a file of the bills you pay by cc, then withdrawing an equal amount from the account, but I like the easy tracking (and it all feeds into my YNAB budgeting software which is nice too).