On the bus this morning I worked out a way to find the shortest route to hit any amount of cushions, I'll have a play with it this evening before I decide if I believe your claim .

if you can hit 11 without hitting a ball, you can do 12 - it's the same, the ball just have to hit another ball just after the 11th cushion and bounce back to the same cushion. it was pointless to make a screenshot because after the 11th cushion the ball is moving too slow, so the number 11 disappears and the ball is over the number 12 ;)

If you figure out a path and a screenshot cannot capture it. Video evidence will need to be produced :)