My sense is that King accepts the idea that the Pats footballs could have dropped ~1.2 psi (on average) and gone illegal (12.5 to 11.3, say) while the Colts footballs could have dropped ~1.2 psi and be deemed legal both times (13.6 to 12.4, say) due to the human element: "0.1 psi is close enough" when they were checked.
Where I think he has strong doubts is rationalizing the lack of common sense displayed by the ref in that scenario. The ref would have seen the same overall pressure drop for one group as he did for the other, after all, despite where the legal/illegal line is supposed to be drawn. The ref should have thought, even though he didn't understand why, that nothing crooked was going on. After all (joking aside), refs tend to be businessmen, lawyers, decently smart people over all, who as we all know do reffing on the side.
My thought is that the ref took a long hard look at the intercepted ball first. This ball was simply an outlier for some reason, 2 psi down (a bad ball, or Colts did something, or maybe it was one that skipped being inspected & inflated, or whatever). Then he just made a rash decision that "something fishy is going on here" and then focused like a robot on whether the other Pats balls were at 12.5 or not. The pass vs. fail tally was what we call "confirmation bias" because it fit the conclusion he had already jumped to, just based upon looking at the intercepted ball.
Of course, the Colts footballs could have indeed been colder when inspected pregame.