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I think the whole "core" thing is part of, as some folks on /tg/ like to put it, "3e ruined a whole generation of gamers."

/tg/ has traditionally hated D&D and its' fanbase.  It's a Warhammer/wargame board for the most part, and most of the TRPG talk is related to WHFRPG and Dark Heresy.  Even the 4e fans there are distinctly not fans of heroic fantasy, and sing the praises of evil (AKA grimdark) campaigns.
The only reason 4e gained a foothold there is at least partially for trolling purposes because the grognards hate it.  The 'core is best' mentality is just a meme.  Where are these mythical players that refuse to make characters with only PHB material, and only fight monsters from the first MM?  If they exist, they are certainly very rare.  The 'core is best' is an exaggeration of the complaining about 'everything is core' of 4e.  A huge exaggeration.  

What people didn't like about 'everything is core' is that a lot of the things meant to be allowed by default were previously optional material.  That is, if you wanted to make a campaign with tiefling characters or NPCs you could, but you didn't need to for every campaign.  Elves and dwarves are implicit to D&D and have been for ~30 years (and the general LotR-ripoff concept of high fantasy before that).  

In 4e if you didn't want that as the DM you had to say "no" (which you are of course never supposed to do), and if you didn't want to play in the freakshow (and increasingly freaky with every new book) implied campaign setting of 4e as a player then you had to play a different game (or a previous edition).  

The same trolls on /tg/ that came up with 'core is best' are also the kinds of players that would rather argue with the DM into allowing them to play their half-dragon kobold necromancer for the entire session rather than pick something else.  The 'everything should be allowed' mentality (and the 'everything I saw in Bleach last week should be in the game' mentality) are far more destructive (mainly because unlike the 'core is best' mentality is actually exists).
Look at the 'what did you like about 3e' thread on these forums.  The most common answer is the abundance of character creation options, and the mention of specific splatbooks that facilitated all of those options.

To the extent that the 'core is best' mentality even exists its' talking almost exclusively about flavour and setting, which isn't something that she getting significantly altered 4-6 times a year with every new supplement that contain new classes and races that are assumed to have always been a part of the setting. 

Feb 28, 2012 -- 8:46AM, greatfrito wrote:

The "core is best" mentality is not something made up by /tg/ - at all.  "Splat books are less good than core books" was a pretty damn common theme everywhere 3e discussion was had (including these forums), and "just material from the core books" was a pretty commonly discussed limitation for campaigns.

Which is fun when you consider Core was likely the least balanced on books ever.

Although a special mention goes to Eberron Campaign Guide, Complete Psionic and Heroes of Horror. 

I think some people (maybe even most?) that are using core "wrong" are probably meaning "I want X to be in the main purchased thingy, whatever that is that is replacing the normal hardbound PHB"/"I don't want to pay extra (beyond the basic purchases) to have this", and/or "I want X to be treated as an important part of the game, which gets a lot of future support".