Except the offseason they drafted Gagner, EIG was flailing about in the media trying to convince everyone that they weren't cheap like Katz insinuated, and tried to give up all their draft picks in offsheets and sign half the UFAs on the market in a goofy attempt to retool quickly and win at all costs.
The summer Paajarvi was drafted, they clearly believed in the team's ability to compete and hired a crusty senior citizen to try and unlock that potential of the declining and apathetic veteran core. They also spent their time chasing Heatley with poorly thought out ideas that they were one winger from competing for a cup.
Neither years were they rebuilding by any stretch of the imagination, and the idea of rebuilding never even entered the picture until mid-way through the 09/10 season when the talent and the roster bottomed out.