Does chess.com have the toughest pool of players?

A few years ago, yes. Mentions of competitor sites were permitted, but comparisons (even positive comparisons) were prohibited. But recently, the rules have been tightened up to the point where you cannot mention the names of other chess sites.

That's the biggest compliment I've ever received

For as long as I've been a moderator, advertising competitor sites has been prohibited; comparisons (positive or negative) have also been prohibited.

Chess.com has chosen the simplest application of simply removing the names of competitors when they appear: more oblique references are also removed if it is still reasonably obvious which competitor is being referenced (which is actually the same standard applied to profanity). Sometimes moderators will make it obvious this has been done by using green text and [Removed], as I have done in the earlier posts; sometimes if it has only been casually mentioned, I will simply replace the text with "another site" or other suitable phrasing without the green colour.

Pretty much the only exception is the name of the competitor in the diagram of a game played elsewhere - those don't get changed, although any direct links to the game on that site will be removed.

If people are deliberately generating work for the moderators in this or any other respect, that's when warnings and lockings will take place.

Those are not chess websites. Those are chess federations who chess.com has no intention of competing with and from my experience, referencing the International Chess Federation or the United States Chess Federation has never been considered a community policy violation. Please correct me if I am mistaken, @david.

You mean FIDE? That's not a site

FIDE, USCF, ECF, ICCF, etc., are federations, not competitors.  Yes, FIDE has attempted to get into the online chess business too, so advertising/comparisons with that venture of theirs wouldn't be permitted, but it's OK to talk about federations.

If there were a lot of untitled anonymous players who could really compete at the very top level, they would occasionally show up to open tournaments and perform at that level.  But Albin Planinc's performance at the 1969 Vidmar Memorial tournament was very much a one-off.

To answer your question, yes. I do believe that chess.com does have the strongest player pools. GMs and “SuperGMs” (2700+ FIDE) play a lot more frequently on this site, than on other platforms. Not to say that these players like Don’t have accounts on other sites, but they do play a lot more games on chess.com. Daniil Dubov is a good example: he is currently ranked #20 in blitz and he has played thousands of games on chess.com. Hikaru has also played more on this site than any other.

The majority of serious chess players (those rated 2200+ FIDE, for example) likely have accounts on most, or all, the major chess sites.

So the "main" pool of online chess players is probably the same, just duplicated across different websites, with different screennames.

Not to my knowledge, no.

Pillsbury's victory at Hastings in 1895 (125 years ago!) is the only comparable case that springs to mind. He was virtually unknown, and faced a world-class array of opponents.

Other examples... Capablanca at San Sebastien 1911, Kasparov at Banja Luka 1979, etc, were all less surprising, because the player who scored the upset victory was already "on the radar". Capablanca had already won a match against Marshall. Kasparov had already played in a Soviet Championship and done well, and so on.

Only Pillsbury and Planinc came completely out of nowhere, and zoomed past all the experienced Masters in the tournament.

So (on the basis of a very small sample set) this seems to happen about once per century.

It would also be much harder in the modern era.  Modern top-level players are playing at a much higher level than in Pillsbury's era.