Lots of teams won one ring but they are hardly elite. Elite is the run New England had and the run K.C. is having now. Anyway, to the extent we were elite at some point it was because of on field results and having a HoF QB and HoF head coach. The front office was the same as it is now. So either you have to admit that we were only elite due to QB and HC or admit that the front office we have now is elite. Personally I think we have a mid-level front office with a bad coach and mediocre QB.
And yes, we don't have the historical legacy of Pitt or the Giants. But, honestly what NFL organizations are elite? Even the ones we think of as elite only win Championships when they have a franchise QB and a great coach. And few, manage to do that past one QB and one coach without a large gap in between. Green Bay did it with Favre and Rodgers is one exception. But even with Love they have been mediocre for the last few years.