I think it's perfectly appropriate for bloggers to criticize public figures, whether it be coaches, players, politicians, actresses, or whoever.
I don't buy the "you have to have been in the field to properly criticize it". That's bunk, and even moreso, plenty of professionals have been questioning Doc lately.
The other part of Doc's argument -- that people should listen to him and his coaching staff about the job he's doing -- is even more ridiculous. What coach is going to admit "you know, I suck at my job, and I'm really in over my head"?
I'm not criticizing Doc's coaching here -- there are plenty of other threads for that -- but his reasoning about bloggers is pretty asinine.
I don't think Doc is saying you have to be in a field to criticize it - I think he's saying it's a bit foolish to give much weight to the opinions of people who have no first hand experience with the field. I notice when this stuff comes up bloggers tend to read into it that they're being told to shut up somehow - they (usually) aren't - instead they're being told that they don't really know what they're talking about, they're full of sound and fury signifying nothing, as the man would say.
I think this is to a degree true and to a degree not - much of Doc's criticisms come from his in-game decisions, which are close to 100% of the coaching the fans see and maybe more like 25% of the coach's actual job. Doc is occasionally slow to adjust or puts baffling lineups together, but obviously he has a knack for creating team cohesion - look at how little tension and conflict there has been this year, it's remarkable. Part of that is the players being willing to buy in to the team concept, but I remember him doing something similar in Orlando his COY season. Additionally, we were the most efficient defensive team, and among the most efficient offensive teams all season, which is an indication of a least a decent set of schemes. Even the "calling plays out of timeouts" criticism appears to have been completely debunked this season.
Fans do have perspective and are often very knowledgeable about what does happen in those 48 minutes, though, so ingame criticisms, especially when a lot of people are saying the same thing, can have some validity.
And I'm not sure what professionals are criticizing him other than your usual suspect columnists - most of the analysis I've seen and heard from ex-players and coaches has been probably 80% positive, and I've never heard anyone at that level even imply he was a bad or incompetent coach.