Can a non-US citizen (or entity) own an N-registered aircraft?
Nothing in the regulations seems to preclude it - but there are some conditions you have to meet per the FAA:


  
  An individual who is a United States citizen,
  A partnership each of whose partners is an individual who is a U.S. citizen,
  A corporation or association:
  
  
  organized under the laws of the U.S. or a State, the District of Columbia, or a U.S. territory or possession,
  of which the president and at least two-thirds of the board of directors and other managing officers are U.S citizens, and
  in which at least 75% of the voting interest is owned or controlled by persons that are U.S. citizens,
  
  An individual citizen of a foreign country lawfully admitted for permanent residence in the U.S.,
  A U.S. governmental unit or subdivision
  A non-U.S. citizen corporation organized and doing business under the laws of the U.S. or one of the States as long as the aircraft is
  based and primarily used in the U.S. (60% of all flight hours must be 
  from flights starting and ending within the U.S.)
  


(emphasis added)

So Toyota could not buy an aircraft and register it to their main company in Japan  on the US registry, nor could they buy &amp; register it under a US Subsidiary and subsequently fly it off to Japan to live out the rest of its days shuttling executives around Asia.
A Toyota executive with Permanent Resident status could buy themselves a nice Cirrus and register it on the US Registry though.