This is actually an excellent question. I perused through my model and some game stats trying to figure them out and am asking.myself the same thing. I don't know if it can be answered without watching their games, but here's what I found out:
My model has their offense rated #6 overall but #126 in reliablility. Good offenses are naturally less reliable, but that number is a little insane to me, so I went into the individual rating for each game.
They had 3 really good offensive games: Boise, Cal, and Utah. Boise and Cal are pretty unremarkable, except that they do have bad pass defenses. Utah is a great defense and they are fairly balanced about it. It wasn't like an outstanding game statistically, but it stands out for the opponent they were playing.
They had 4 really bad offensive games: Arizona, ASU, OrSt, and Wazzou. Arizona and Oregon State are good defenses, the other are unremarkable in any form. Now what makes Arizona and OrSt different from Utah is that they stop the run first and make you one-dimensional. Washington did okay running against both teams, but they ran the ball less overall, which may have cotributed to the bad showing. However, the two teams that Washington didn't run the ball well against all season were ASU and Wazzou, and it was their worst games offensively.
So (before watching the games) I do think there is some truth to them being reliant on the run.