Re: What's the chord at 12:08 ?
You can hear it definitely has an F and a C in it the way that guy played it, and I know the chord at that point in the song is a G. As for what the dude in the video actually played, who knows. It sounded to me like he was playing a C-rooted chord (b3 of the song), and then went b3-4 for the following two chords leading back to the 1, while the song is supposed to be on a G there (the b7 of the song), and go b6-b7 for the next two changes leading back to the 1. In short, the video dude sounded a fifth off, in terms of what chord roots he was using for that part.
As for what Page played, I believe that the notes Gtrjunior posted sound correct (though the chord name from that tab he quoted is clearly wrong, and probably the fingering too). Listening to the recording, you know there's, at the very least, higher octaves of C and F. The rest of the chord is obscured to my ears, but the 4 and the b7 stick out like sore thumbs.
In short, I thought the dude played the formation in the first pic I posted. But the second pic makes more sense as for what Page might have played on the recording.