Inadvertant Whistle Question

[rockyroad]

Varsity game last Friday night...opposing QB throws a backward pass to running back flaring out of backfield (yes, it was clearly thrown backwards)...RB falls down and pass sails over his head. Our linebacker runs in and scopps it up and takes about two steps before the Line Judge blows his whistle and signals incomplete pass...the White Hat immediately runs over for a little discussion with the LJ, and then tells us it is an inadvertant whistle and the down will be replayed...so here's my questions: since the whistle blew after we had recovered the ball, shouldn't we have retained possession? Doesn't the offensive team get the choice to replay the down or take the result of the play? And since we had the ball when the whistle blew, doesn't that make us the offensive team?

Note: the white hat very clearly told us that it was a backward pass and the LJ had no business blowing his whistle and (his own words) we were screwed out of a possession...but when I asked him these questions, he just got a confused look on his face and walked away...