More likely, the story is designed to make the public believe that US propaganda is actually aimed at the "foreign adversary" rather than at the US population. The emotionally appealing bit is the idea that even if the story is fake, Iran is now thinking it is dealing with an adversary that has and is using tech that is right out of science fiction.
In reality, it's all aimed at us, the people. All of the "tough talk", the comments that appear intended for dissident groups within Iran, etc., is all meant to mislead the people (us) who can stop the war so we don't do so.
Why would disinformation about a technology used to recover a pilot have any bearing on public socio-political views about the war? Eternal September is becoming increasing real on HN.
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The us did recently announce that it has technology that can manipulate space and time or something.
It's very likely a psyop like you said. "You don't know how advanced we really are! When we come for you you better just give up!"
I bet the us does have some secret weapons technologies. I wouldn't be surprised if some of them are sci fi adjacent. But I think their biggest asset is likely intelligence, and channels to mass manipulate people via the Internet and boots/agents on the ground. Fortunately for other countries that power is more effective domestically. Unfortunately for us citizens there are trillions of dollars developing technologies to destroy us and not enemies.
The shift in us politics is directly related to feeding this. Defense/offense companies need to make more money. So they need to use these tools. Us citizens are the likely next targets beyond things like software exploits and taking over a few countries seemingly randomly.