I agree with this. In fact, I don't know that there is a huge correlation between military service and potential to be a better policeman. Many former military guys I work with seem to be fairly rigid in their thinking, unwilling or unable to use discretion appropriately and unable to make a decision independently. It's ironic because this is the very attribute I hear about when people talk about former military in police: "They can make important decisions quickly without supervision." Some of them can, some of them can't. I don't see any huge difference in the decision-making ability of military vs. non-military. Many of them are more worried about "chain of command" than they should be and have no problem with passing the buck upwards when they should have made their own decision. Not saying this is true with ALL former military types, but it is far from a given that someone with military experience will make a better policeman than someone without.
Also, don't forget the many, many specialty jobs in the military that have nothing to do with leadership. And some of the absolute WORST mid-level managers I've seen in law enforcement were former officers in the military. I've noticed that those guys are the ones who seem to be more likely to rely on their rank to get things done as opposed to earning the respect of their subordinates.
If there are a lot of former military types in civil service jobs, it likely has more to do with the veterans preference points available on the civil service tests and the fact that federal grant money often funds the hiring of veterans. Not necessarily that so many places prefer military experience because vets make better cops and firemen.
Here's a question I have for cops: Management often picks a guy to be their "hatchet man" to administratively go after employees who they've designated as a target. Have you noticed that a disproportionate number of the guys they pick for hatchet man duty seem to be former military officers? I wonder if the "mission first" mindset makes them more willing to screw their colleagues for the sake of their own ambition?