Identity of "supersonic"

This closing dialog kind of caught me thinking. I was watching a program on the Science Channel about military aviation, particularly on the history of the Harrier Jump Jets. At the end of one program segement, the narrator said " The Harrier has one disadvantage: It can't fly supersonic."
I know if we go by the rules of the "book", "supersonic" seems wrong as it appears to be an adjective, which should be an adverb (supersonically) to modify "fly". That said, I've also learned that the rules can go sort of reversed in contexts dealing with stative verbs, in which adjectives are allowed to modify verbs described as follows.
http://www.englishclub.com/grammar/adjectives-order_2.htm

• The examination did not seem difficult.
• Your friend looks nice.
• This towel feels damp.
• That new film doesn't sound very interesting.
• Dinner smells good tonight.
• This milk tastes sour.
• It smells bad.

These verbs are "stative" verbs, which express a state or change of state, not "dynamic" verbs which express an action. Note that some verbs can be stative in one sense (she looks beautiful | it got hot), and dynamic in another (she looked at him | he got the money). The above examples do not include all stative verbs.

Now, my curiosity is, "fly" is no doubt a dynamic verb which requires an adverb ( fly supersonically). May I have the experts' take on this usage? To me, both seem possible, (it can't fly supersonic / supersonically), depending on how the listeners set up the antena to their ears. I guess!

Thanks