Sedin won the Hart largely because "Henrik is still scoring while Daniel is hurt" made for a good story, not because he was "most valuable to his team." It was telling that Daniel had practically the same season the next year and finished second to Perry, who had a less impressive season than several of the guys Henrik beat out. Someone brought up OV's win in 2013, and that was the same thing. "OV has a monster second half (well, quarter) after observers had left him for dead" made for a good story, but he was not the most valuable player to his team, either.
That was a pattern in the first half of the 2010s, where the PHWA was casting votes on the basis of what was sexy to write about, rather than following the actual award criteria.
if things are close, monster second half will almost always win the hart over the consistent guy who was the favourite all year. in the post-gretzky/mario era: pronger over jagr in 2000, theodore over iginla in 2002, forsberg over naslund in 2003, thornton over jagr in 2006, henrik over ovechkin in 2010, perry over daniel in 2011, ovechkin over crosby in 2013,
i can think of three exceptions—two are because the guy who took the art ross at the end of the season didn't make the playoffs. that's MSL catching an injured crosby in 2013 and jamie benn with his five point game in 2015.
the other one is a special case: jagr in 2001 caught sakic in the art ross race and had a crazy second half. but obviously the mario variable worked against him.
Most valuable to his team is a crap metric. It is so vague as to be meaningless. The most valuable player is the best player, and with a few very notable exceptions, has generally been voted on as such.
Well, Henrik wasn't that, either.
the goal post of most valuable to his team is open-ended enough that sure you can definitely argue that henrik sedin was that. that team had a pretty hard road in the 2010 season. their goalie, who happened to be the captain, flamed out in the elimination game of the previous playoffs. (the canucks had three different leads in that game, and daniel sedin in particular had a fantastic game to keep bringing vancouver back, until luongo let in two goals in a minute with seven minutes away from possible victory and ended the season on three straight blackhawk goals and the hats falling for patrick kane.) there was also a leadership vacuum, with sundin's retirement, the most senior canuck/sedin mentor mattias ohlund gone to tampa bay, and the pressure of being captain and goalie really weighing on luongo. and the really underrated thing is this all happens with the complete and total distraction of the olympics in vancouver.
then daniel goes down and henrik basically steps into that role that sundin vacated and becomes the team's de facto captain. somehow pulls himself into the top ten in goals while keeping the team afloat (11-7-0 with daniel out). there's a very good argument that that run, as statistically not super impressive as it was, was what made that team realize that they weren't just the guys hanging back limiting shots on luongo (who, remember, basically was the canucks gameplan before this), they realized that they could hang with anybody in the league.
i mean obviously you could make other arguments that ovechkin or crosby, or one of the elite goalies, was the most valuable to their teams. but you can certainly also make the argument that henrik was it too.