Launches from international waters from a US firm will still need FAA approval
Many aspects of SpaceX's rockets are covered by ITAR, which puts strict regulations and controls on the exports of many aspects of SpaceX's vehicles.
I imagine exporting the rocket to a non-US based firm would be a much larger bureaucratic hurdle than getting FAA approvals.
This leaves me (and hopefully you) wondering what ITAR actually still accomplishes. I guess federal contracts dictate the use of the ensuing technology? I still see issues with that depending on how IP rights are assigned.
I guess we're waiting on the next PGP-style test of export control laws.