I was always taught that a tyre had to have the legal depth of tread over 3/4 of its width to be legal. Doesnt matter if the outside edge is bald, or "feathered" as its known. If it had exposed cords then yes it was an illegal tyre, but if not Id hazard a guess theyre having you on. Have you still got the tyre? Will be difficult to proove its the same one as the one examined.
*edit* im sure it used to be the case that the police couldnt simply stop you for no other reason than a "routine check", they need a reason, i.e suspected of being drunk e.t.c. Not sure if this law is out of date though. No you didnt keep the tyre..
