Savard was not traded or demoted, he was on the team for the previous season, was still under contract at the end of this season, and was injured to have his games total limited.
As Art said there is the discretionary option, if Boston sees fit to go to the league and lobby on his behalf, and the league agrees then I see no problem.
I did a little research for personal reasons (off topic of Savard) because I was wondering if the Penguins won the Cup last year if Crosby would have had is name on the Cup again even with his injuries....yep, played exactly 41 games. At least according to NHL.com
Thing is, he does qualify based on the rules. The team is allowed to petition the Commisioner for his inclusion, which they did and were given the green light.
He was a contributor in the locker room, as much as an equipment manager or assistant trainer, both of whom will get their names on the Cup. I wouldn't have a problem with it, and apparently the team feels his contributions were vital to their playoff run. So even though I don't feel he should automatically be included, I vote yes.