It seems the Iranians were in two minds about this..
First , they tried to turn this episode into some kind of a major " diplomatic incident ", by trying to present it as a US intrusion into their airspace, similar in a way to what they did in the not too distant past with the incident of the British Royal Marines when their boat allegedly strayed into Iranian waters.
Then, for reasons so far not entirely clear, they seem to have changed their mind, and decided to call it a day, forget about it all, and all of a sudden find out that the plane was not American after all, but a Hungarian private jet with completely innocent intentions.
The only logical explanation , in my opinion, is that this is yet another example of different camps within the Iranian security and political establishment trying to score different points with different agendas.
Obviously, someone in Tehran thought that this incident might provide them with a golden opportunity to create a "crisis situation " with the US at an extremely unsuitable time, and then exploit it politically to the maximum.
In contrast, somebody else, high up, decided to the contrary, that this is probably not the right time to enter into a dispute with the US at this particular moment, hence the whole episode was put to rest.
It will be an extremely interesting example of how the Iranians will be dealing with various situations as they come by in the future.