Detroit didn't even need to win. As soon as their game went to OT, the Flyers were eliminated. He gifted the game to the Caps and screwed Detroit. If the Caps would have lost in any fashion, Detroit would now be in the playoffs.
I just got back last night from a trip to San Diego to see my granddaughter, but I did keep track of the Caps while I was gone.
From what I've heard, Detroit tied their game about a minute before the Flyers went empty net, but the staff didn't know about that until it was too late. My feeling is, Detroit had only themselves to blame. If they had handled the Canadians instead of having to come from behind at the end of regulation, Philly would have likely known they were out of it and played it straight. But as long as they thought they were in contention (and with a Detroit loss, if they could have scored they were a Pittsburgh loss away from the playoffs) they had to try to go for it.
And besides, that situation was only appropriate karma for the scheduling disadvantage the Caps found themselves in going into Philly. Having to travel and play a back-to-back road game against at rested team as the last game of the season was a tough row to hoe.