I have heard that the depth of field depends only the the f-stop and the magnification. Is this true?
Yes, under some conditions. When the subject distance is small with respect to the hyperfocal distance, the front and rear depth of field are almost equal and depend only on the magnification and f-stop. As the subject distance approaches the hyperfocal distance, the front depth of field gets smaller and the rear depth gets larger, eventually extending to infinity.