Dave,
I bought my first of these" errors" from Jim McFadden when they were first in the machine. My friend Larry Trostle played for a bunch of the strikes and got many rotated, some reversed,and some "normal" strikes. He sold me some and the centers seemed okay on the ones I got. He said they came from the strike machine that way. That would seem to confirm your theory that they came from the mint or cage. Larry has passed away but I am sure he would not have altered those strikes.
Pete