Doubt the White House had much to do with it. The MV-22s are used for 'green side' missions only, and will not carry the POTUS. Only the VXX (/VH-92) will perform 'white side' missions, with all the inevitable build/testing rigors that creating a flying Oval Office entails.
Actually the White House/DOD has a strong and undeniable control over HMX-1 within the 'system of checks and balances' in place here in the U.S. (which often do not work as they were intended). The system gives authority to the DOD under the control of the Executive Branch to stop funding of projects just as the Congressional Branch (House and Senate) or the Judiciary Branch (Supreme Court) can do. The Executive Branch (Whitehouse) did not override the decision to integrate the V-22 into HMX-1, and in fact they actually originated the decision to do so through the DOD.