I don't recall what the original debate was about, but yes, he did run it more against the Pats* than against the Texans. But I think it's considerably more complicated to explain why he did than to just say he made more of a commitment to the running game. There are too many factors to count. Things like injuries (who's currently injured for us, who for them), matchups (how do our guys match up man-for-man against their guys, are there particular advantages or disadvantages against each team), defensive styles, and so on, that influence the guy's decision on how much to run. It may have been that he felt Cordy was struggling early against the pass rush, so throw a few more running plays in there to get his confidence and game feet back. Maybe same with Urbik. Maybe Wilfork was causing too much trouble with the pass rush, so he tried to run it a little more to keep him honest. I have no idea.
Whatever it was, the circumstances made Chan believe he would be better off running more against the Pats* than against the Texans. That doesn't necessarily mean if we ran more against the Texans that we would have done better.
But again, I have completely lost what the debate was about here, so I may just be making your point.