By some incredible chance, a photo was captured of that very moment. Here's what Chessbase had to say: "In the above picture Anish has the captured piece in his left hand, while executing the move of the capturing piece, his queen, with the right. He then went on to press the clock with his right hand."
Thus, it is clear and I'm sure most of us lightning aficionados have committed the same exact mechanics. That is, we pick up a "capturer" piece with the right hand, pick up the "capturee" with the left, then press the clock with the right hand to complete the move.
So on what grounds was Epishin protesting? No doubt he had in mind these two.
4.1 Each move must be made with one hand only.
6.8b A player must stop his clock with the same hand as that with which he made his move. It is forbidden for a player to keep his finger on the button or to "hover" over it.
There is also Appendix B5: "The arbiter shall make a ruling according to Article 4 (The act of moving pieces), only if requested to do so by one or both players."
Look, I don't mind rules myself, but frankly - the strict application of 4.1, in blitz, is nonesense. It's time that we adjusted the rules for blitz so that 4.1 isn't strictly followed. Here's a couple of arguments for it, and I swear I'm really serious.
The first is that using both hands allows for more accurate placement of pieces. An obvious benefit is that we minimise any confusion over which squares your bits are sitting. Secondly, two-handed play reduces the incidence of knocking pieces over. This is because a player is able to nicely grab a single piece instead of two. It's especially the case when capturing a taller piece. Try it, capture a Queen with a pawn, say, and you'll see what I mean. Finally, that using both hands generally only occurs during a time sramble tells us that it we're basically outlawing a behaviour that is, in fact, pretty rare. So why not simply rid our tournaments of one more reason for an entirely unnecessary dispute?
But, the singularly most convincing argument of all is that this is blitz! OK, so the guy moved with both hands. Who cares? I tell you who. Whining pussies.