Solution: After almost getting a handle on Shoots from distance in FM13, the madding PM is back with a vengeance this year. And there is no solution, but I did make a few interesting discoveries about it.
I almost always watch my matches on "comprehensive", but when I'm testing a crazy tactic, sometimes I'll speed through it. And I noticed that my side had 9 corners in the first 7 Minutes of a match. Since this wasn't a tactic that relied heavily on wide players, I wondered what was going on. And it turns out that in this ME, the large majority of corners are generated when the keeper tips the ball wide, or over the bar.
And one thing we know about this ME is that there is still plenty of opportunity to score from corners. So one of my favorite tactics in a long time came into being. It involved quick tempo (which increases shots from distance), short passing (more possession equals more shots from outside the 18 yard box) and the "shoot on sight" instruction, which no one ever uses. Add the strategic signing of a few "shoots from distance" shameless gunners, and viola! My personal record is 51 shots on goal. But a funny thing happened, which is this tactic won kind of a lot.
My theory is that the ME gives a match rating boost to anyone who puts a shot on target. If you're shooting and failing to score, but the keeper is saving them, your players ratings start to creep up, and the ME says "this player is having a good game" his moral and confidence skyrockets, and lo and behold, he bags you a goal.
This is only a theory, but spare a moment for shooting from distance next time. It can work better than you think, and it will generate you a few extra corners to take advantage of at worst.