Before the fight, Tony Stark was acting like they can somehow impose the Registration Act on Thor. You do not treat a sovereign State like that. Which means the US government do not really see Asgard as a separate government.
Thor got angry and kicked the snot out of Tony Stark.
Then Tony Stark "proposed" a "compromise"....he said - "if we treat Asgard as a separate entity, like a diplomatic mission or embassy, then it's not officially United States territory -- especially since it's technically hovering eight feet above US Territory. That would put Asgard and anyone who lives there outside the jurisdiction of the Registration Act, and give you diplomatic immunity....An approach along those lines would make sure my SUPERIORS DON'T LOSE FACE, and that would be necessary to sell this. How's that work for you?"
First of all, it's not an official act. Tony Stark was just proposing a possible compromise.
Second, Stark himself said that he would need to sell (or convince) his SUPERIORS to treat Asgard as an embassy. He doesn't have the authority to outright grant embassy status to Asgard, nor to grant diplomatic immunity.
Third, this line "especially since it's technically hovering eight feet above US territory"....tells me JMS has no proper grasp of how sovereign territory works. The territorial sovereignty of a country do not end over eight feet above the ground. The territory of a country comprises all land, bodies of water, and the air space within its territorial jurisdiction.
And at the end of the issue, they were still monitoring Asgard. One of Stark's aides even ask what should they do to Heimdall. Stark just said "let it go". Not because he recognise that Asgard is an embassy, he just didn't want further confrontatiom with Thor....and later on, in SIEGE, didn't SHIELD attack Asgard? Sounds like they do not treat Asgard as a separate sovereign territory of another