They probably told their communicatons company that they shot down the big Cats and it wasn't the US that shot them down, just to save face.
But if the Cats never fired, then obviously, they would be in quite a predicament. But that's why the US military spends millions upon millions of $$$ just to train our fighter pilots in situations such as these. Our pilots would certainly not put themselves in that kind of danger without taking action. It does pay off.