I think you're right on with this. They appear to be using a military round from a specified distance (lots of cheap target practice) that is not normally used for sniper work and does not even lend itself to long-range varmit hunting (highly accurate bolt action rifles). They are taking their shots at certain times of the day (they've been well-trained) and they are selecting random victims (terror).
IF it were someone that gets their rocks off "hunting people", they would be getting the thrill of the long distance shot and would be using varmit calibers and rifle from a much greater distance. Calibers such as a 22-250 or even a 25-06 or a host of other "prairie dog" rounds.
I think LEOs know exactly what they are dealing with and not sharing it because of the mass histeria and outright backlash that it would cause in society. But I think it's only a matter of time before everyone knows anyway,.