They do have that reputation. I heard a lady ask a (retired) Texas Highway Patrol Officer why there was never a cop around when some idiot came weaving through traffic and past her at 30 mph over the speed limit. He replied "That's him, he's just off duty."
I hate to say it, but I was the nemesis of the Street Department. I was always watching down alleys, streets, behind businesses and must have hit 100 parking meters, signs and cars. Caught a LOT of burglars though.