That is the key right there.
You see most of the cycling world wrote Froome off as a useless git who would never amount to anything on a bike. This was an opinion held not just by his fellow pros, team managers, and fans but Froome's own mother. Brailsford has a keen eye and saw something everyone else missed. Even though Froome was struggling to finish stages, sometimes holding onto motorcycles to make time, Brailsford noticed that the total distance Froome travelled as he zigged and zagged up the road during climbs was roughly 80% more than the distance everyone else was riding. Taking distance into account, Froome was the fastest man in a race.
Brailsford employed British ingenuity to fix the issue. He knew that a regular cycling coach could not handle a problem of this magnitude. None had ever worked with someone as monumentally incompetent at the skill of riding a bike as Froome, who made Fernando Escartin look like Fabian Cancellara. He would have to go outside of cycling to find a coach who was an expert at maintaining a straight line. That's when genius struck. Swimming! Swimmers spend hours going back and forth in a straight line. It was almost too perfect.
He hired a swim coach and a training plan was quickly devised. It consisted of forcing Froome to ride up and down a long and narrow hallway somewhere in Yorkshire. At first Froome could barely do it. He would careen off walls, banging into one side then bouncing over to crash into the other side. They had to start with but one lap per day. Any more and Brailsford was afraid Froome would injure himself. Gradually the distance was increased to two laps then three then five then ten. Slowly but surely Froome got the hang of it and learned to ride in a straight line and, just as Brailsford predicted, Froome's speed was unsurpassable.
Now you know the rest of the story.