Nope. Some require a letter from either an MD or a DO, and some don't require any physician letters at all.
Just from my personal experience, UMDNJ-SOM doesn't require either letter, and PCOM "strongly recommends" a DO letter.
But if you don't shadow a DO, be sure you do a lot of research on your own so you can discuss osteopathic medicine in your interview without looking clueless.