You likely just lost the bet - sorry.
Cross commissioning is remotely possible, both from the Service Academies and ROTC. However it is remote.
http://www.apd.army.mil/pdffiles/r145_1.pdf Read section V starting on page 44.
From the SA it is possible too. An AFA Cadet is commissioning into Marines in May. He is an olympic shooter at the AFA.
A small part of the Regulation...
6–34. Appointment in the U.S. Air Force or U.S. Marine Corps (other than Regular Marine Corps)
Graduating Army ROTC cadets may be released from the Army to accept appointment in a component of the USAF or USMC if one of the following criteria is met: a. The cadet has served 12 months or more of active duty in the Service concerned. b. One or both of the cadet’s parents are currently on active duty or a retired member of that Service. c. The cadet’s spouse is a member of that Service.
Note this does not indicate the officer is commissioned in the Army and AF/USMC at the same time.
Once commissioned, the regulations regarding Interservice Transfer apply.