Not making it out of the first round since their Stanley Cup victory, the Capitals were desperate to add to their roster with limited cap space, and with Kane's situation, he was an ideal fit for many contending teams: if they were willing to risk a disruption to their locker room.
Kane, at the time of the Oilers' elimination, led the playoffs in scoring, a definite contributor to their run. His physical play and scoring touch would mesh well with the Capitals style of play, similar to Ovechkin and Tom Wilson.
Of course, the Capitals were unable to sign him this last season, but with knowledge of Ovechkin's desire to have Kane as a Capital, perhaps it's something the team re-visits in the offseason, as Kane again is set to become a UFA.