There are at least three very real things that COULD (as opposed to DO) affect a pitcher's penchant for icky innings.
(I just love playing games with words; and I didn't even grow up reading the Old Testament in Hebrew!)
1. Problems that come with pitching out of the stretch. You roll along retiring consecutive batters until you don't, at which point your mechanics change. Some might struggle with this more than the average pitcher.
2. Problems that come with the distraction of baserunners. During your consecutive batters roll you focus exclusively on the batter and executing your pitches. But once a runner reaches base your attention is at least dual. Some people handle this better than others. Me, I can't walk and chew chaw at the same time.
3. Problems that come with mental brittleness. Not everyone handles pressure equally well. Not everyone handles bad breaks equally well. While overall there may be a statistical reason to minimize this, any human being who has lived, breathed, worked and played in this life can vouch for it's reality. So it doesn't make sense that suddenly you step on a baseball field and it's a non-factor.
I don't doubt there's a certain amount of statistical noise when we notice what seems to be a pitcher's tendency for his shirt to completely unravel after a thread or two is pulled. I also don't doubt that all pitchers play in the 1960's rock band, The Human Beinz (for real, there was such a band). As fellow humans it shouldn't surprise us if some pitchers suffer from this malady. We all know family members, friends and coworkers who are emotionally more brittle than most.
Of course whether or not this applies to James Paxton is a separate matter, as is how often we might actually run into it in a population such as MLB pitchers where there is a lengthy weeding process of "one shall be taken and one shall be left."
Thanks for interacting on the subject, Doc. It's always stimulating to listen to someone who knows more about a subject than me.