Football isn't a magical black box, of course advanced analysts can understand what the coaches were trying to do on each play, don't be naive. In fact, PFF has ex-NFL coaches and players consulting for them in grading, that's why they took away our (general public) access to Premium Stats. They are making a killing by selling it to NFL/college teams exclusively because it's so valuable (which pissed me off but I understand it's a business). Their grading may not be perfect but it's good enough to spot trends and use descriptive stats to predict outcomes. For example, Brady's 2 throws on 4th down vs Denver and Gronk's amazing catches. To a normal person, that seems out of the ordinary but it wasn't out of my expectations because if you know that Brady was throwing TDs under pressure at a historic rate in 2015, then you expect it to happen. If you know that Gronk is the undisputed #1 from a talent and grading level then you expect him to make plays like that in double coverage. You expect Von Miller/Wolfe/Jackson/Ware to eat up any offensive line they face if they're not on the field for extended periods of time (like Peyton's 4 pick game).
Belichick's quote is only an analysis of an individual talent level (his players), but how does that talent compare to the rest of the league? For example, there's no way he can know that Dion Lewis had forced more missed tackles than any other RB in the league simply because he doesn't watch every snap of every game. If you showed BB tape Jamaal Charles, Marshawn Lynch, Adrian Peterson, and Dion Lewis could he accurately predict which back would have the most missed tackles by game 8? Game 13? No, of course not. That's why advanced stats are so valuable because it provides perspective relative to the rest of the league. You may think Nate Solder is hot shit and he may have been in college, but compared to other linemen at his position he's below average. As the season goes on, we get more and more data as players face more and more opponents. Combine this with historical performances and you have a pretty good idea of who is top 5 at their position. For example, Jordan Reed was getting great separation even before his injury. When he came back, he continued where he left off. But he was an obvious one, how about Delanie Walker? He was a top 3 graded TE this year on a horrid team. Yet nobody knows who he is or even what team he plays for, let alone how good he was this year.
NE's Shaq Mason graded positively because he did his job properly more often than not on every single snap of the game. This is regardless of his reputation as a poor pass pro lineman, he still did well in the game. That's why you have to look at a micro-game level vs season level performances and try to identify trends. Did he just have a good day? How did he perform in the next 3 games? 10 games? Like Aaron Donald outperforming JJ Watt. How many of you have heard of Aaron Donald? Most would say that JJ is a better player, but we cannot definitively say that now based on the past 16 games. Aaron Donald is an absolute force, and if you saw him break Justin Forsett's forearm you know what kind of power he has. Watt is still playing at an obscenely good rate but he now has company on the mountaintop. In summary, I want to know if Shaq Mason can continue his above average play vs Denver and that would be what BB would wonder as well.
Nate Solder and Dion Lewis will make the team better from a rushing standpoint, there is no disputing that. But for the pass game, it's not going to make much more of a difference. Brady simply needs more pass pro, not rushing IMO. If you give him a half second longer to throw to the best TE and best possession receivers in football then you don't need a rushing attack, which NE showed this year. Case in point, the game ending 2pt conversion. Gronk was open in the end zone but Brady didn't have time to find him nor did he have time to even scramble. NE isn't running the ball on a 2pt conversion, even with Solder and Lewis on the field. They won the majority of their games going pass heavy (unless they played a weaker run stopping D and exploited that) and either play to their strengths (passing) and/or the other teams weakness (bad pass defense or bad run D). There's no way they're risking a run on a 2pt conversion against the #1 run D in the league, BB's not an idiot - he's going to play to his team's strengths and play the percentages. I would give the Pats a 25% chance of converting against the Denver D with Dion Lewis.
You say advanced stats aren't everything, but I would contend that they describe 90% of what you're seeing on the field. They include every facet of the game from every snap from the play the offense was trying to run vs both teams' formations. Every player either did his job or he didn't and to different magnitudes. Over time, the superior talent will separate itself from its peers.