While I agree that you don't have a complaint about the fact that they didn't hold the plane, there are a few unanswered questions.
Was your flight late, or did you simply miss the connection because of an exceptionally long wait at Customs? If your inbound flight was late, AND it was not due to weather or ATC, it seems to me that you would have a reasonable expectation that US pay for your stay in PHX tonight. If it was due to weather or ATC, then you really have no recourse at all.