The question is:
If a player deliberately creates a character that is more or less munchinized, does it give the GM a permission to allow the NPCs to use the same methods?
No. The DM
always has the right to use those methods, whether the players do or not. The reason he
shouldn't is not "the players don't do it", but because hitting the PCs with overpowered stuff is likely to lead to a TPK, and more than a few TPKs will lead to the players quitting in disgust.
Now, that said...
Ideally, the players and the DM should discuss power levels between them, and in particular expectations regarding min-maxing. If they all decide they want to min-max to the hilt, then that's absolutely fine, and go for it. If they all decide they
don't want to min-max and prefer a much less optimised game, that's also fine; go for it.
The problem only crops up when one member of the group decided to min-max well out of proportion with the rest. In which case you have an
out-of-game issue. And it's a bad idea to use in-game solutions for out-of-game problems. The thing to do is to speak to the player and ask him to rein in his power-gamer impulses, to perhaps redirect his system mastery away from 'optimising' areas of the game and towards 'fun' areas of the game. But, basically, deal with it that way. But if he refuses, you have a problem player on your hands - in exactly the same way as if he insisted on playing a Neutral Evil Assassin in an otherwise Good party, or a LG Paladin in a party of Assassins. In which case, if he really refuses to fit with the group, then it's better to drop the player. As hard as that may be.
This is why the Gentlemens' Agreement is a poor solution to broken stuff. If one player munchkins up, the DM is forced into this awkward position, which will likely end badly -- especially for those players who chose not to munchkin up.
Much better to go to the root of the problem: fix or nix the broken stuff!
So, 'other,' I guess.
The problem is that in an option-heavy game (like 3e or 4e) you can't fix or nix all the broken stuff. Because when you depower one combination, this has the effect of simply making another combination optimal - your power-gamer will simply migrate from the one to the other. Worse, very often the individual elements are fine; it's only the combination that is problematic.
It's far better simply to acknowledge that if a player
really wants, then they can and will find a way to break the game. Put that to them, and point out also that it would be better for all involved if they
didn't. The overwhelming majority of players will then have sufficient respect for the group not to destroy the game. And the rest you don't want to play with anyway.