I find my live blitz and long ratings are not too different from my OTB.
Turn-based depends how serious you take it - I'm low enough because I spent about a minute per move and sometimes have 50 games on the go.
Bullet is inflated here as well for some reason. But non-bullet live chess seems to be strikingly similar, and I know a few others who play in 'real-life' and have similar OTB classical ratings to their blitz ratings here.


My thoughts on it.
In my own experience and I strongly believe that it is the same with the majority of other players that there is not much inflation comparing online ratings and otb provided players play the game fair and square.
Because they're different pools of players, the ratings aren't the same everywhere. ICC and maybe also FICS have a rating survey you can add too by submitting your online and OTB ratings. It's not letting me view it right now, but I think 80% or so of players are within 200 points (some higher, some lower, and as much as 20% not even within 200 points).
For example, here, the top of the blitz rating pool will be 2200-2300, the top of ICC is 3000+ Yahoo! maybe 2100-2200, etc. Of course this isn't only at the top, but speaks of the players in the middle too that their ratings can't be 1:1 with other sites (although as you say the extremes are always less accurate).
I also compare my play against fide rated players who are 2000-2100 and the strength is more or less equal.
But their FIDE rating is for long time controls against serious players... hard to compare to throw away blitz games. You see yourself that your rating can vary depending on the time control (as it is for most people). I know for myself I play more attacking and gambit type games in online blitz that I'd never go for at a tournament. It's hard to believe you can compare your blitz play to someone and then believe it will hold true also for tournament standards.
2. Players who can play 2000 in blitz is sure to play better with more time like otb.
This makes it sound like you've never played in an OTB tournament. Long time controls are very different. If you're mind is used to blitz, your thinking can be too fast and unstructured for long time controls... the point in standard games is accuracy and doesn't have much to do with speed. Strong blitz play doesn't have much to do with a strong long time control game.
Also because the games are so much longer, you can fool yourself and over think, or get tired and actually make blunders you would never make in blitz. I've been there (and seen others do this) so I know.
After playing both format ie. OTB and Online that's my assumption. It actually happens in my own game.