In general, there are a few schools that are biased against people from area studies programs (like Middle Eastern studies or American Studies). These programs are often less stable financially, and dependent on the good will and cooperation from many different departments in order to work. Sometimes that results in a powerhouse known nationally for its rigor, and sometimes that results in programs being established only to be reabsorbed by departments when the administration messes up and/or funding runs dry.
Chances are, if you go into Middle Eastern History, you'll be able to take classes in all fields -- Middle Eastern Literature, language, sociology, geography, anthropology/archaeology, etc. and get credit for them. Do find out before you apply, but this is the case with all of the places I applied to and where I've ended up.
And if you pick a place that has both a history department strong in Middle Eastern faculty, and a Middle Eastern Studies program, you can often get a special certificate that works similar to the way dual majors work in undergrad.
Also, your former prof isn't wrong. Often, history departments have the most funds out of the humanities and their students are better taken care of. These departments have more say in administrative processes and tend to be on the larger side, and these advantages will trickle down to you.