From most articles I have seen, US 'Combat Pay' come from their Defense Budget. At least they get that at $250 per month, qualifying time = 1 day.
And, can we really blame Joe Public for not understanding the military? If they are against Gov't policy, they are not likely to be supportive of the Armed Forces are they. As with riots, strikes etc; I've never understood why Joe Public attacks PC Plod, it's not as if the Police closed the coal mines or are running G4 summits is it.