Georgetown also handles a lot of the media relations duties when they host. Hosting isn't as simple as saying that you'll throw your logo on the court - there are actual responsibilities that come with being the host institution. That wouldn't keep somebody else from hosting (it's not like it's on Georgetown's campus or anything), but if Georgetown wants to host, they'll get right of first refusal.
There's also nothing keeping Maryland from playing at Capital One Arena, and they actually did play there in 2002 for the first two rounds. Georgetown, however, could never play in Capital One Arena, even if another school hosted - NCAA bracketing regulations prohibit teams from playing in any venue where they played at least three regular-season games.