Yeah, people are getting confused here and allowing some of the very bad journalism to colour their thoughts.
Andrew Mitchell almost certainly did behave badly, swear at the cops and probably said something along the lines of pleb. He has a history of altercations with the police, and other bullying incidents, including swearing and belittling them, and even an incident involving his bike previously apparently. There were a number of friends who took the stand who all admitted he swore a lot. Furthermore this has been investigated and the judgement found to be that something basically did happen along those lines.
Also, the judge didn't base his entire decision on the comment re the police mans speed of thought - it was just a pertinent, and probably accurate, point that the policeman would have had to have thought up a very specific and very out of character insult incredibly fast based on the timings of events and footage.