What are they trying to hide?Nothing. Read the source, and then check the link giving MESA's actual statement. What they're saying is that Middle Eastern institutions won't want to work with students who will then be obligated to go on to work for American defense and intelligence agencies.
Again, if this is something where the students involved are undergrads that are going to be learning Arabic, etc., from local resources, then I don't think that there should be a problem. But if we are talking about graduate and post-graduate students, who will be working with institutions based in the Middle East, then I can see what their concern is.
Sounds like a bunch of professors (most of whom are radical anti-Israel types) trying to protect their rice bowl with the typical silly arguments. We are supposed to believe that Middle Eastern governments can track the majors of American college students without institutional cooperation? Their parents can't even do it!
Ivory Towers on Sand: The Failure of Middle Eastern Studies in America by Martin Kramer discusses the problem in depth. As has happened in so many other disciplines ravaged by political correctness, reputable Middle Eastern scholars are going to have to migrate to the think tanks and institutes that now give the university radicals such well deserved competition.