The point of the saying is to consider how hard you are working to turn your skis, and how much are those skis turning you as a result of your work.
13 m isn't that long, and 9 m is even shorter. At 30 mph it takes less than a second to traverse 13 m, and about three seconds to complete that 13 m radius (and I mean radius) turn. Just say'n. There's plenty of room on the hill to carve some fine arc-2-arc turns with shaped skis.
Even if you aren't carving arc-2-arc, the same mechanisms that make skis carve turns are at work making you turn, if you just tip your skis and engage the edges/bases, without trying to turn those skis.
If you are on hard snow on shaped skis or even if you have a straight ski in soft snow, so long as the ski bends under load, tipping it will initiate a turn (change in the direction you are going), without you needing to turn (pivot about an axis perpendicular to the snow) the skis.
Contrary to what some may have had indoctrinated into them through having come up through a system, and then teaching in a system that values client safety, teaching folk to keep their speed down, the true joy of making some turns comes not from keeping one's speed down; it comes from controlling one's path while increasing one's speed, fulfilling the natural desire and instinct for power and control. It's fun to have fun, but you have to know how.