If that's your definition of a "great" GM, that's cool. I'm not the one who outlines the characteristics and traits that are necessary for every single person to consider a GM "great."
How about this: Over the last decade, can you name 5 NBA GMs who have clearly done a better job than Joe Dumars? That includes those who are no longer GMs now. Name 5 who clearly have done better jobs as NBA GMs. You have probably well over 50 GMs to choose from with firings and hirings (I'm guessing), perhaps more.
Maybe you can. But, I think you'd be hard pressed to do so. I think that's how I'd probably define a "great" GM, by comparing what that particular GM has done to what other GMs have done. Really off the top of my head, RC Buford might be the only one who "clearly" has done a better job. Edit: And of course Jerry West...
Look at a guy like Mitch Kupchak who was gifted Pau Gasol, otherwise he'd probably be out of a job right now. Or a guy like Danny Ainge, who was widely considered a bumbling idiot before Kevin McHale threw him a life line. Look around the league and identify the good and great GMs. Look at Kevin Pritchard who was being hailed as the next bright mind, but look at all the luck he has had in the draft and then look at the debacle he has from his off season moves.
"Great" GMs make mistakes. It's the nature of the job. In Dumars' case, a couple of his mistakes were monumental so they get more attention. But, if you go and look around the league, who has clearly done a better job over the last 10 seasons?