Apart from the parts which were not designed in the US, sure... Your definition of "American" seems to be based on feeling, not some sort of solid definition...
I'll walk you through my thought process...
Per Wikipedia: "It is being designed and built by an aerospace industry team led by Lockheed Martin." Now correct me if I'm wrong, but Lockheed Martin is an American company. Therefore it must be American.
I'll use another industry as an example. If Samsung produces 75% of the technology inside a television, and then sources the plastics from say China, it's still a South Korean product, not a South Korean & Chinese product. Or a car manufacturer, say Lotus, that sources an engine from Toyota, don't start saying their vehicle is British & Japanese. It's just British.
I'm not saying that the JSF project is only American, but in design and manufacturing and the majority of the funding was in fact, American.
How is what I'm saying based on feeling? It seems to me, you're trying to argue a point you can't substantiate either...