US Military hardware is far from invincible. Also, most drones are designed to be expendable, so stealth isn't a high priority. Sats exist, sure, but can view a limited number of targets of interest at once.
LotsOfZeros is right, Iran is good at propaganda. See: PressTV
the serbs downed a stealth bomber using Russian AA.. allegedly. But it's not really confirmed whether this was an accident, or wheter a single nullet migtht have managed to get a lucky shot or whether indeed it was AA.
The stealth bomber isn't entirely invisible to radar, but where other aircraft will give off a really obvious fingerprint that it's an aircraft, the stealth bomber might give off a pixel or two, so conventional radar cannot tell whther it's an aircraft or a bird or whatever.
It is possible though to use both visual and radar technology as a combined effort in order to track stealth. but this hasn't really been test much. The stealth bomber hasn't been used against a modern military in a long time.