Who is lying about the costs. Certainly not my local government with our 70 man police force. If all or the US wanted to chip in money so we could have more actual sworn officers (not military show troops), I am sure the city would accept and spend the money. But, we are asking. We handle our own, as best we can, mostly within our means.
Nobody is lying about costs of putting thousands of active duty troops on the street and most people do have some idea how much money being wasted on show. Hell, I am so old, I have sat at a desk counting out to the dollar, actual dollar bills wrapping them in LES (Leaves and Earnings Statement) after being up all night counting the hundreds of thousands I had personally signed for when I picked up the bulk pay. I definitely know what troops cost in just pay, not counting transportation, food, billeting, administration, medical, dental, equipment, etc, etc, ad noseum.