I think both of those points are true.
FIDE vs Chess.com ratings explained

This is nicely done. I do not have a Fide rating, but bullet range between(1950-2050), Blitz(1975-2115), so my estimate FIDE is ±2050. In my country i am rated above 2000 Nationally, normally Fide rating is higher than national ratings, as most guys play daily chess, and play tournaments, but almost never play fide tournaments - thus never get a FIDE rating. I am an example, suppose to be 2000+ fide, but only played one or 2 Fide tournament in my life.

The linear regressions gave me nasty flashbacks of econometrics classes. But if you're still around to read this: kudos. This is great work.
I've always believed in one size fits all. O.K , it's internet chess and there are cheats, but where on earth is the harm in applying standard Elo to all? If you cannot earn a title through internet chess then why the f*ck does it matter if Elo is used?
I don't even go to a chess club. I use this bullsh*t Chess.com rating system to get a rough idea of where I am. If I was brushed with the Elo brush I'm sure I would be sh*t.

If I would use myself as comparison, despite I don't have an Elo FIDE I've played with several friends that have and I believe my level is around 1900-2000. My Blitz rating here on the other hand is around 1700's, so I suppose there is a 200 points difference between them.
Chess.com raised its live ratings 150 pts, to make it like the USCF ratings. So, if your standard chess.com rating is 1700, your FIDE is 1550, because USCF ratings are 150 pts higher.
I have to say, these are frighteningly accurate... at least regarding me.
According to each of my ratings (excluding daily, because I timed out the last 50 games), I would be placed somewhere around 1900-2000 FIDE (my chess.com rapid is overrated, should be a bit lower with more games).
My USCF is 2000+, but my last performance rating was 2300, so I would estimate my true playing strength in 2014 to be ~2100 USCF.
After a two year hiatus, I've clearly gotten rusty, so it makes sense for my rating have dropped down ~100 points. If we say my true playing strength right now is around 2027 USCF ~ 1927 FIDE, then all these estimates are ridiculously close (within like 50 points)
Bullet estimate -> 2022 FIDE
Tactics Trainer estimate -> 1919 FIDE
Rapid Estimate (Given actual rapid rating 150 pts lower) -> 2005 FIDE
Blitz estimate -> 1911 FIDE
Avg: 1964 FIDE, which seems accurate.
Given the limits of the data set you CLEARLY stated, I find your analysis statistically valid. And fun to read as well. Thanks for doing this

Great thread. Thorough analysis, given the limitations of the data. Nothing to nitpick about, from the statistics side.
Two questions though (not sure if you're still reading this, but I'll give it a shot):
a) the game categories seem to have changed names, compared to when you wrote you analysis (in 2013). Since I'm not on this site for so long, could anyone give me a brief mapping of the current names for time control <--> names used in the analysis above?
For example, what is "Chess.com: Standard"? What is currently called: "Live chess", with standard time controls for Live, so 20/20? Or is what is now called Daily, so correspondence chess?
Similar for what OP calls "Chess.com: Online". Is that "Live" now? If so, which exact time controls?
b) I find the breakdown by rating classes particularly interesting, because it seems to indicate that at the lower rating levels, chess.com ratings are overrating players' skill compared to FIDE, while at higher levels, they seem to underrate actually. Assuming it's a valid result, and not an artifact of reporting error, I wonder what the reason is for that.
Also, ideally, I would have liked to see a more fine-grained breakdown, say, by steps of 100 points instead of 300. But I understand that the data probably didn't allow it.
Thanks again for taking the time for this analysis. And apologies for the necro of a rather old thread.

Thanks for the quick response!
The "online" really confused me, I imagined it would have to be a tight time control.

Actually standard is both rapid (for example 15m10s) and longchess such as 45 min + 45 seconds pr move

Actually standard is both rapid (for examole 15m10s) and longchess such as 45 min + 45 seconds pr move
I believe that zanglebert wanted to know how the V2 game designations correspond to those in V3. Note that there is no designation "long chess" in either version of the site's interface; anything played live at time controls longer than blitz is called "standard" in V2 and "rapid" in V3, even if the game is played at classic OTB controls (not that I've seen any such games :-).
Actually standard is both rapid (for examole 15m10s) and longchess such as 45 min + 45 seconds pr move
I believe that zanglebert wanted to know how the V2 game designations correspond to those in V3. Note that there is no designation "long chess" in either version of the site's interface; anything played live at time controls longer than blitz is called "standard" in V2 and "rapid" in V3, even if the game is played at classic OTB controls (not that I've seen any such games :-).
I have played many such games. 45+45 is a good option for when I have loads of time (like on Summer vacation)
aman_makhija, I saw that you improved a lot here in may, june, july. It takes more time before the fiderating is up to date when you are improving. Fiderating will be somewhat behind for players who improves a lot, and describes a strenght that was some months ago.
And you are maybe more comfortable online than in tournamenthalls.