Are there any privately owned V-22 Ospreys?
There are no 'private' Ospreys thus far (all are operated by USAF, USMC and JSDF)- the Bell Boeing MV-22 Osprey used by the US Marine Corps's HMX-1 presidential helicopter squadron:


  ... will conduct presidential support missions, which means these aircraft will carry presidential support staff and news media representatives travelling with the president," the USMC says. "The Osprey mission at HMX-1 does not include carrying the President of the United States."


so I'm not counting on 'luxury' interiors. When (and if) a civil version of V-22 is produced (or if the Japanese feel like selling theirs), you can buy it and make the interior whichever way you like.