The crucial question here is whether Jelavić received the ball after it rebounded to him off an opponent, or if the opponent played the ball.
Because the Laws of the Game define offside as (Law 11, p. 33):
A player in an offside position is only penalised if, at the moment the ball touches or is played by one of his team, he is, in the opinion of the referee, involved in active play by:
- interfering with play or
- interfering with an opponent or
- gaining an advantage by being in that position
We are talking about the last point in this case. And, in the official interpretation of the Laws of the Game (p. 102), it is defined thus:
“gaining an advantage by being in that position” means playing a ball that
rebounds to him off a goalpost or the crossbar having been in an offside
position or playing a ball that rebounds to him off an opponent having
been in an offside position
The referees obviously decided the Irish player has played the ball, therefore, this was not an offside. And I would say this was a correct decision, given the time it took the ball to pass through the defense line – it was not a quick rebound, the ball stopped there for a second. (But I could not find a close-up video of what exactly the Irish player did with the ball.)
After the question was amended: Note there is no such thing as “active” and “passive [offside] position” in the Laws of the Game, those are just jargon terms. For an offside to be called, the player must be “involved in active play” by one of the three exactly defined activities listed above.
The first one was definitely not the case here:
“interfering with play” means playing or touching the ball passed or
touched by a team-mate
The second one is slightly closer, but still, no go:
“interfering with an opponent” means preventing an opponent from playing or being able to play the ball by clearly obstructing the opponent’s line of vision or movements or making a gesture or movement which, in the opinion of the referee, deceives or distracts an opponent
Jelavić did not obstruct anyone’s line of vision or movements, and he definitely did not deceive/distract the opponent, since the Irish defense probably did not see him at all.
Which leaves us with the last option debated above. None of the three points was fulfilled, therefore, no offside.