Take the tyre to a tyre fitter and ask if its legal, if it is get writtten proof and appeal. Plod should have taken numbers off the tyre to identify it.

His knowledge seems suspect if he thinks brake fluid is a points issue.

But if he's on a bike he's probably already done at least 3 years in a traffic car.

Tyre law is 1.6 over 3/4 width for the whole of the circumference, no tread required on the remainder.