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Fixed.

Setting aside Big 12 silliness, I think the answer has to do with the way narratives can harden.
The Heisman is a storybook award, for bad or for good. It goes to someone with a story. Ohio State's is complicated.
OSU spent most of the year as a disappointment. It's biggest failure was on a big stage against a so-so team, and the enduring image of Haskins was throwing again and again. He became the gunslinger doing what he could with a bad defense and not much running support, but it remained in the context of disappointment. The big non-conference win evaporated. And there were stats, but they always had that looming over them. Sadly, that doesn't get a guy a Heisman.  
And in that, we probably underrated what OSU and him were doing. I had a friend who is an ardent OSU fan, one who is often levelheaded, and when the Michigan game came around, he said something like "If Michigan can't beat, THIS Ohio State team ..."
Of course THIS Ohio State team was 10-1, No. 8 in S&P. But they couldn't shake that feeling, even on here. As such, what should've been a big win in The Game became more of a referendum on Michigan. The BTTG didn't help, with a team destined to get loss No. 5.
Basically everyone, including many of us, treated OSU like a disappointment right up to the end, and by the time that could shift, there wasn't enough runway to fully throw things back into a positive gear. If something like the Michigan game happens 2-3 weeks earlier, I'd bet there's a better chance Haskins is contending and maybe there's a more real discussion about a playoff spot.
(It also brings into relief the situation in 2014, where OSU got the defining win at the start of November and benefitted from the Big 12's split/lack of a title game)

I don't recall QB rating ever being much of a factor in Heisman races

It's not necessarily QB rating being a deciding factor, but that QB rating is the measure of the aggregate statistical "reasons" a voter would cast his ballot for Murray or Tua over Haskins.
Haskins has the volume.  Great.  More yds, TDs,...but on a lot more attempts.  
Haskins had the most yards on the 2nd-most attempts.  Murray was 3rd in yards and not even in the top 20 in completions.  Haskins first in TDs?  Murray was 2nd, on 150 fewer attempts.  Murray was more efficient, nearly matching Haskins' volume stats in far fewer opportunities.  
And all of it ignores the vast advantage Murray had running the ball, both in yards and TDs.  He was even 7th in the country in yards per carry.  
Haskins' season would have won him a Heisman in the 90s and even the 2000s.  But in the past 5 years, a season like his has become more and more common.  He wouldn't have beaten Mayfield last year.  Bu Rudolph had a similar season.  Goff did.  Mahomes did.  Watson did.  Passing stats have gone astronomical lately.
It's easy to be blinded by his "arm talent" and potential NFL career, but alas, the Heisman is a collegiate award.  So Mr. 5'9" baseball player Murray gets the trophy...because he earned it.