The problem has nothing to do with qualifying for Social Security.  The problem is that once you have any Medicare coverage -- including Part A, which is free -- that disqualifies you from having an HSA.  There are some major employers who keep their older employees as long as they keep producing income (I'm thinking of a large stockbroker here) and don't remind them that they may have lost eligibility at age 65.  I have seen some continuing to fund an HSA until they're 80.