Why is a foxhunter's red coat pink?

Some foxhunters, depending on the hunt, are permitted to wear "hunting pink." It's usually limited to hunt staff, and sometimes only to male hunt staff.

Hunting pink involves absolutely nothing of the color pink. It includes a red coat, white breeches, tall boots and a white shirt.

Not everyone uses the term - but why did a red coat come to be called pink in the first place? The traditional etymology says that at one point the very best hunt coats were made by a tailor by the name of Pink.

A hunt leaving a castle - yes a castle - in England. The man in "pink" (red coat) is the Master of Hounds; the other riders are wearing black. Source Owain.davies via Wikimedia Commons.