Croquet World has a an article on painting boundary lines in North America. Frankly, I didn't even know this was a debate. The answer for the USCA Rules is simple .... the ball should be out of bounds when it touches the boundary. I know, that makes it hard to get behind a ball for a rush. However, I've been told that the USCA games was intended to be hard. Or just move the margin to 10 inches. I doubt the nine inch boundary was determined by how it affected the game ... it was likely just the average length of a mallet head.
So, I would frame this as paint is strongly preferred and string lines are acceptable at shared facilities.