Congress is the one demanding a face-to-face meeting, if I read my news correctly.
But to answer your question more directly, NO, they don't all work in Detroit, especially if you consider the "support staff" they'd likely take along (albeit some of the support serfs would travel on commercial flights) for a meeting of this kind. Mulally (Ford) lives in Washington state and "commutes" to Detroit. ALL of these guys work in Detroit, Chicago, New York, and elsewhere to maintain contact with suppliers and "business and financial markets" and are only "nominally headquarterd" in Michigan.
A few (quite a few) years back even I did business with major GM divisions in Massachusetts, Washington, Illinois, Arkansas and Wisconsin - without ever seeing Detroit - shortly after I had the pleasure of destroying testing a Chrysler truck on an Arizona test track while one of my associates was doing about the same to a Ford.