IT'S BOTH
Seating to a set depth allows consistent strike, but primer ignition can vary with the resulting crush variance. So pocket cutting to a set depth is a prerequisite here. The next is actual primer height(they all vary). Having a K&M primer seater, you should be aware of their indicated model that zeros out variance in pocket depth AND primer height to achieve correct crush.
With same pocket depths, same crush, and best adjusted strike for the primer, I think proper seating is pretty much covered.
But one other factor, is time. Seated primers tend to back out a bit within a few days, and there has been recent testing that showed this continuing for a few weeks(at an ever dropping rate).
I've seen this enough with Lapua, Norma, and Tubbs brass. But I haven't yet tested for specific impact of it from day to day.
There is more to primer firing than merely 'sufficient'..