The notion of the distance going up a steep hairpin is not so 'clear'. Yes, you can measure the shortest distance, but it is often pretty bad to run the shortest distance if it is very steep because the gradient is so steep on the inside. The road surface can also be rather slanted. In bike racing you usually go a bit more into the middle on the steepest turns.
One time trial up Mt Baldy I was passing a guy who starts several minutes ahead of me. As I caught him he tried to maintain my pace, which he did for a while. Then we got to the hairpin turn and it was so steep that I heard a 'thunk' behind; I think he went to the inside line a bit and was going so slowly that he could not maintain balance (the upper end of the switchbacks, where the road averages 10% gradient and on the insides of the turns is probably almost twice that.
By the way, they are using that road for an Alpe du Huez -type of finish at the Tour of California in May.