See
http://www.snopes.com/politics/obama/airplane.aspAlthough Senator Barack Obama flew on a variety of aircraft during the long campaign season, from March through June 2008 he primarily used a Boeing 757-200ERaircraft chartered from (and operated by) North American Airlines as his campaign plane. During that period, the plane bore the standard color scheme and company markings of a North American Airlines aircraft:
However, once the primary campaign effectively ended and Senator Obama became the presumptive Democratic presidential nominee, his campaign plane underwent a month-long refurbishment to prepare it for the general election campaign, a process that included reconfiguring the interior seating and modifying the exterior markings to identify and publicize the aircraft as Barack Obama's official campaign plane. The latter activity included replacing the North American Airline color scheme and markings with the Obama campaign slogan ("Change We Can Believe In"), the BARACKOBAMA.COM domain name, and Obama's sunrise/flag O" campaign logo<.>
The replacement of North American's commercial markings included the removal of two stylized U.S. flag images which are used in the airline's logo (a registered trademark). The North American flag/logo on the forward portion of the fuselage was removed and the one on the tail was replaced with the Obama "O" campaign logo, while traditional depictions of the U.S. flag adjacent to the plane's registration numbers remain<.>
In short: Obama removed REGISTERED TRADEMARKs of the airlines, but kept the traditional U.S. Flag, as is on all U.S. planes.
Update: I did not mean to imply that your post was not accurate. It is, of course. I just meant to provide the source for the WHY of Obama's changed plane.