Certainly the government admitted to shooting down the plane.
Admission, in a legal sense, usually implies not only admitting the facts, but also that there was an error or wrongdoing by the party doing the admitting.
And this has not happened.
Its also really hard for the US to offer an apology to Iran
Oh, um, yeah. Maybe they could offer an apology to the relatives of the people that got killed? Most, if not all of them, never took any hostages in any embassy. Some of them weren't even Iranians.
Nobody can say the US didn't admit to shooting down the airbus, and the US government did offer up an explanation.
And that isn't an "admission" in a legal sense - since they give themselves an acquittal in the same paragraph.
People may not like the explanation, or agree with it, but at least the US stood up for its actions.
If you call giving yourself a complete acquittal "standing up to your actions", yes.