So, the point tims4wins made was that in retrospect the Patriots would have been better off kicking FGs in Denver. That is simply true as a retro-analysis matter; you can add up the points and see (at least, based on any realistic set of assumptions about FG%). However (and I think this is where you are getting lost) that observation is different than saying that since they would have been better off in Denver kicking field goals looking back on the game (with different knowledge than when the decisions were made) that must mean they change huge numbers of decisions going forward. Also different than saying "the decisions they made last year were wrong". If I hit on 20 in blackjack it is a bad decision---but if I get an ace, I can also say that in retrospect I was better off hitting than not.
No one is saying the decisions in Denver were terrible. No one is saying that they must have changed their model radically. No one is saying that the sole reason they left time on the clock Sunday was because they tried to run out the clock against Seattle and they lost.
What I think is being said is that they look at a ton of data, and they likely are self-scouting and trying to figure out whether they have calbrated their decisions correctly. They are likely constantly adjusting. The Patriots have access to a ton more research and information and analysis than we do, so its worth reflecting on what that might be and how (if at all) it might change things. Everything I am aware of about how they scout, cross-check, research, and make decisions suggests to me that they are very self-critical and thus they are, in fact, looking at these past games and evaluating them rather than just assuming they were right. My personal suspicion is that they'd do the Denver game the same way, and that they'd focus more on scoring than time against Seattle. I think Sunday's game is wholly consistent with the second of those, though we don't have enough info to say that's causal of course.
I'm just speculating, because I haven't looked at the data anywhere near closely enough to have a meaningful point of view (nor have you, though you seem to think you have). I would guess they spend time trying to figure out all sorts of things as part of that self-analysis, like what sample to use, how to adjust it for their own strengths and context, etc. rather than just taking NFL-wide assumptions. I would guess they have a way to think about higher scoring games as opposed to lower scoring games. And lots of other complexity. I personally think it's very likely that "they were evaluating the correct factors both in Denver and Sunday" as you conclude, but I also recognize that I don't really know what they looked at, and thus if or how they might have adjusted their thinking.
I like Barnwell and win expectancy tools and think they add to the discussion. But I also recognize that if people treat those things as truths, it's not so...and the guys who build the models will tell you the same.