I didn't say that only pilots with military backgrounds were better at Police work. Equally they are no better at any other type of civilan flying.
What you and others seem to fail to realise is that when a Police unit is looking at recruiting a pilot then a candidate with 1500 hours of varied military flying will always be a more attractive proposition than a 1500 hour civilian flight instructor or offshore pilot. This is purely because the ex-mil pilot will be a known quantity and has been through a proven system, has military discipline instilled, has a varied flying background and generally will be someone that will fit in with Police operations.
Also other members of the unit will undoubtedly know the person or can find out a great deal on the military grapevine. One of the most important aspects of a succesful, small, ASU is that a person fits in. If they don't it can be very uncomfortable experience for all concerned and a bad apple can be very difficult to get rid of.
BTW I may be ex-mil and and ex-Police pilot but I now fly offshore and in a previous life I instructed as a civilian on the R22. I don't tend to comment on aspects of the industry that I am not familiar with.