of course we export our advanced weaponry. buying the plane is just part of the process. once you own it, you need to have ground support, computer and communication capabilities, not to mention spare parts, and engineers to support the process - most likely on lease from the manufacturer. pilots are important but just one part of the equation.
selling complicated weaponry like planes is a great way for countries to foster dependency. you would have to be pretty stupid to go to war against the US using American planes. you wouldn't be able to fly them for long without mechanical support (parts etc), engineering support.