Yeah. The owner needs to be a US citizen (includes both human beings and entities). There is an exception for certain foreign corporations (those that do not qualify as "citizens").

Adam, have you actually asked an aviation attorney what would be involved in doing it? And what the liability to friends would be in a co-ownership situation? I kinda doubt ferrying a plane over would be cheaper (why would you have to deal with Delaware?)

Sorry, not a clue about the TSA question.