What was usually not reported, especially in the mass media, was the technical details of these battles. The U.S. aircraft were not allowed to use their major advantages; powerful radars and long range missiles. The reason is simple; these systems enable American aircraft to knock down the opposition before the opposing pilots can even see each other. The U.S. is not the only nation with such capabilities, but the American radars and missiles have characteristics that the United States would prefer to keep secret. The thing is, when it comes to weapons based on electronics and software (like aircraft radars and long range missiles), you don't want potential foes to know details about what your stuff can do. Additionally, spreading the rumor that your aircraft and pilots are not world-class badass aerial warriors, is valuable as well. This is the ultimate in Information Warfare, as it lulls potential enemies into a false sense of confidence. This actually works, at least based on the play the Israel and India "defeats" got in the foreign press.
Of course, if your own politicians demand to know what is going on, you take them into a classified briefing, and make sure they leave revived and satisfied. Otherwise, you aren't going to get the billions of dollars it takes to develop and build all those neat gadgets, and then recruit and train the pilots that can handle them.
Some of the air force generals in foreign countries know what's actually going on here. But if you can sell something to the general media, even politicians in dictatorships have to deal with it. So, while Chinese spies are constantly trying to find out details of U.S. fighter radars, missiles and pilot capabilities, their own media, and many of their air force generals, go on about how badly the Chinese air force is going to whip those Americans, if it ever comes to an air battle.
The U.S. Air Force and Navy have, over the last decade, adopted the practice of conducting mock air battles with friendly countries. In these battles, the American flyers usually get beaten by the locals. This made big news when the victors were Israelis or Indians.