In the Comprehensive Rules 4.0:
initiative
At any time, either one side or the other side has initiative. The Free Peoples player has initiative while he has four or more cards in hand. Otherwise, the Shadow has initiative. If there is more than one Shadow player, then all of those Shadow players have initiative when the Free Peoples player does not.
Also, there is no mention of initiative in the definitions of regroup phase, reconcile, discard, discard pile.
From this, I'd agree that when discarding to reconcile, initiative can be lost. I think the important text is "At any time".