Did you miss the amount of management/coaching decisions that showed the top brass in the organization didn't care about losing? The players, especially Jack and Sam, were carrying the team to wins as best as they could without a coach (Bylsma) that wanted to engage his own players, to the point where the GM has to step in and punish the players for things, while the organization did nothing to support them with anything that resembled a chance to try and build a winning roster. They weren't given a chance to win.
After 2+ years of seeing that writing on the wall, and you have a chance to bring in Veteran Leadership at the coaching position and management, the team hires a first time GM, and First time NHL Coach. It would be very tough to show you care, when your development, and sense of winning is being undercut by management/coaching. Then they trade away a guy in ROR, that had a history of doing whatever it takes to win, and play winning hockey, in favor of a coach that was teaching losing habits and making the organization a pit of despair to come to the rink for, ONLY to then fire him the next season.
Jack and Sam were toxic BECAUSE the Sabres organization MADE them toxic or show toxic "actions". They bred that sort of culture on the team. Unsurprisingly, the guys that showed "negative" responses to losing, turned out to be successful where they went next. While the players kept here, because "they wanted to be here" stayed terrible.