Sorry Cliff, but you completely missed the point. You are (probably, it's not really relevant) right about how the officers started getting free coffee.
But the stereotype? That started as a result of the differentiation between police and the public. I implied this initially, perhaps I should have stated it.
When every member of the public pays for a coffee and then an officer goes in and gets one for free it creates segregation. This fosters jealousy and resentment for the police in the view of the public.
Don't treat them like God's and maybe they won't act like it!