It does happen, actually. Mostly just boredom, but the police do pull people over for no reason.
And it's not ridiculous, in fact i'd say it's the most likely explanation.
i once got pulled over for being too young (26?) to own a nice car (a 4 year old 1.2 fiesta). I was at the side of the road for almost 30minutes while they checked my details, my GF's details, and kept telling me "i must have a reason" to be out etc. The driver of the police car was a right tool getting angry when i said we wasnt going anywhere, while the female officer in the front questioned my GF, the two other coppers checked every detail of the car like tyres numberplates etc.
But a year later i was pulled over at 3am as a quick check due to ST's getting stolen all the time. And had a nice chat with the guy.
Basically from what Fett has said hes done absolutely nothing wrong, other than maybe speeding to speed up the overtake, but that isnt the offence given. I dont understand the whole thing.
Was the bus/coach tailgating the unmarked car?