What you say here is only PARTIALLY true. These agencies usually use Remington 700 ACTIONS, not rifles. I'd bet that 90%+ get some serious custom work done before they'll shoot well enough to be put into service. Most police SRT/SWAT sniper units require < 1MOA ALL THE TIME. Not average, but every single time, including the cold barrel shot. The Marine Corps uses the 700 as the basis for the M40 sniper rifle, but after it leaves the armorers at Quantico there's really not much Remington left in it.
The way I put it is that the Ford/Chevy in your driveway is a Remington 700, the rifle that the Marine Corps uses is a full blown Nextel Cup stock car that just happens to carry the Ford/Chevy name.