Well - if the racer can't arc to arc and he doesn't blow out, then the racer did something other than arc to arc...
It can be redirection, stivoting etc. I don't like "Pivoting" as it is too generic - you can feather and redirect the skis in many ways...
Likewise, the recreational skier - they don't have the issue with turning on a specific line, but if he or she can't control the speed with arc to arc on the given slope, then they'll do something other than arc to arc. Be it redirection, stivoting, hop turns etc.
Other than a racer chopping off the line, they're all variations of mini-hockey-stops!
Anyone can do hockey stops...
Plain physics: skiing is about direction and speed control... and they're both about ski-snow interaction.
@asolo - if you don't re-engage the skis, it's just one big steered turn. So, the best way to learn stivots is to focus on carving
. Then do hockey stops without actually stopping. Then do them more to the side.