The changes made in 2014 to the FIVB rules contain that basically any touch of the net is treated as a fault. Does this "any" also include passive, unintended contacts, for example if the ball flying into the net pushes it against a player standing on the other side of the net? Or is such a touch still considered legal (or at least not punished)?
First of all, it’s far from “any touch of the net is a fault”. The actual rule (11.3.1) is that “Contact with the net by a player between the antennae, during the action of playing the ball, is a fault.” (emphasis mine). The next paragraph explains the action of playing the ball includes take-off, hit (or attempt), and landing.
That includes touches by the attacking player, the player blocking him, etc., but it excludes e.g. a blocker on the opposite side of the net who was confused by a fake attack. Even though he wanted to block the ball, his contact was not a fault, as he was actually not near the ball, so he was not in the action of playing it.
Also, it excludes touches made when not playing the ball at all. For instance, if a blocker lands and then turns, touching the net with his shoulder, it is not a fault, the touch has not occurred during the action of playing the ball. However, if a player interferes with the play, even outside the action of playing the ball, that is a fault. (For instance, a player tripping and then using the net for support.)
As for the specific question you ask: if the ball flies into the net causing it to hit a stationary player on the opposite side, it is not a fault. However, if the player has deliberately moved his hands close to the net to alter the rebound of the ball (preventing the opponent from recovering the ball from the net in case of remaining team hits), I believe this could be called a net fault. (It would definitely be a net fault in beach volleyball.)