Your understanding is correct, at least for a family plan. Individual (no family) might be half that much.

Of course it's stupid, insipid, idiotic, and childish to have to jump through hoops to get the additional $800 but you knew that already. What you might not know is that claims can still be denied for what might seem to be arbitrary reasons, and you have to fight for reimbursement. If you ignore requests for supporting documentation your access to funds will be completely cut off and your benefits suspended, meaning you can't use your HSA for anything whatsoever until you placate the mindless bureaucrat denying your claim. That's your Caring value right there.

Sorry for the rant but it's justified. Dealing with our insurance has made my wife literally break down in tears on multiple occasions.