[Update by your friendly BullsBlogger, 09/09 : Here's the official announcement (via SBNChicago), the names mentioned below plus another former Bulls scrub (not that he can't coach), Rick Brunson. Brunson's greatest achievement in the NBA was providing inspiration for the once-fantastic but now-dead NBA satirical site RickBrunson.com. ]
Griffin played his final season and a half (followed by a cameo in Seattle after the trade deadline that second year) as a Bull, known as (and sometimes even played like) a defensive specialist and solid locker room guy. His initial acquisition was one flashpoint of the Bulls character > talent philosophy of the Paxson years (a rep less deserved now, probably), given that Pax dealt away J.R. Smith for only cap space (and two second-rounders) in order to sign Griffin.
Griffin really couldn't play anymore at that time, but that didn't stop him from being put on the floor, earning him the unintentionally bestowed BaB moniker of 'A-drain'. I suppose that's a testament to his ability to mesh with coaches, and it was fitting that merely a season after being out of the league he reunited with his Bulls coach Scott Skiles to join his bench in Milwaukee before receiving this promotion back to Chicago.
But as much as he was touted as that solid locker room influence, he was part of one of the more famously dysfunctional locker room incidents in recent Bulls history. After seeing rookie Joakim Noah suspended in response to a verbal confrontation during practice with then-assistant coach Ron Adams, Griffin and fellow veteran Ben Wallace petitioned the Bulls to suspend Noah an additional game, a strange and seemingly unprecedented turn of events.
That entire season, of course, was a disaster, though Griffin escaped most of the blame compared to that put on Wallace, and likely rightfully so. While I'm interested in hearing Noah's take on this hire, I'd guess that history has either been long-forgotten by Noah (who's seemingly a different person now compared to then) and/or the Bulls made sure he was consulted on the hire. No sense peeving off your second most important player, not to mention that Ron Adams himself has already been re-hired by the organization as well. (why get that band back together? who knows, but Adams has a solid rep only enhanced by his most recent work in OKC)
With Griffin essentially replacing Pete Myers on the bench, and given Griffin's history with the Org. (though he did play for the Thibodeau-assistant-coached Rockets in his career as well), I don't doubt he'll serve as the spy for Gar Paxdorf. That's not an indictment: every team has that guy that can communicate to the front office what the coach can't (or won't).
What bothers me isn't Griffin's history as much as his inexperience, and moreso the inexperience, or at least lack of stature, of Thibodeau's staff as a whole. Myers' departure did require a 'players coach' for the bench, and Griffin seemingly has the tools to be excellent at it, but I'd be more comfortable with another hire in addition to this. Right now Adams is the lead assistant, along with another Thibodeau hire Andy Greer, and then Griffin and (rumored to return) big-man coach Sidney Green.
This worry exists against the backdrop of Thibodeau himself never having held his current position. Then again, VDN was given high-paid well-known assistants in Del Harris and Bernie Bickerstaff, and those guys seemingly were effectively retiring a couple years early in that role. Maybe this is an intended new direction.