I think everyone's opinion of what a "classy" organization is may be a little different. For me, it comes from the top... Mara keeping his hands off of coaching and draft decisions (as opposed to the Jerry Joneses, the Al Davises, etc) and not hiring douches like Rex Ryan, Brandon Marshall, etc.
Coughlin is what he is and that's an above-average coach with a Super Bowl ring. Yeah, he may not be a "people person," but he's better than 75% of the guys coaching in the league right now I'd say, and his teams are always well-prepared and play hard. I'll take results over a "people person" any day... NO WAY do I want to go back to a Jim Fassel. I also find it notable that the only people who complain about him are veterans who seem to think they deserve special treatment. Toomer lost a step; Jacobs has lost a step. That's why they were replaced, not because Coughlin isn't personable.