Is this continuation of D85, Gruenfeld Defence, Exchange Variation, tenable? I am watching some commentary on the World Championship Games. This is from Game 1:

[FEN "rnbq1rk1/ppp1ppbp/6p1/8/3PP3/2B5/PP1Q1PPP/R3KBNR b KQ - 0 8"]
[White "Anand"]
[Black "Carlsen"]


The commentator states that Carlsen has several moves available to him at this point, including one which confuses me: 1. ...Bg4. I see that it stops White from castling, but after 2. f3 that Bishop seems silly. The pawn structure looks unfavorable but not fatally so after a bishop retreat. Alternatively, White can also play 2. Nf3, 2. Ne2 or 2. Be2 to set up an exchange.

What's the deal with 1. ...Bg4?
I have little idea about the Gruenfeld (hopefully someone who is more familiar or a better player than I am can give a more complete answer), but a few points you may have overlooked:


After 1...Bg4 2.f3, as you say the pawn structure is marginally weaker, but there's also a bigger problem of how white will develop the g1-knight. Nf3 is now impossible, Nh3 looks bad and if black's bishop stays on the c8-h3 diagonal he can then give white doubled h-pawns. Ne2 might look plausible,  but there's then a problem of how to move the knight from there. c3 and d4 can't be reached without a move vacating that square first, which will probably require other preparations as well, Nf4 too soon is dangerous as it could force white to make even more concessions in pawn structure if Bh6 is allowed, pinning the knight to the queen. Finally, g3 is a poor spot for the knight as the g6-pawn takes away two future squares and e4 is already being taken up by a pawn.
In grandmaster praxis, a draw with black is a respectable result, and trading off the bishops after 1...Bg4 2.Be2 gets black somewhat closer to this result.
1...Bg4 2.Nf3 gives white doubled pawns after the exchange, and the half-open file that results isn't that useful as it faces onto a reinforced pawn. It also leaves the knight on e2 (assuming white does not want to lose castling rights or lose the d4 pawn) with the same problems as mentioned above.