Perhaps you are referring to Physics 61-65 at Stanford, which lists “Recommended prerequisites: Mastery of mechanics at the level of AP Physics C and AP Calculus BC or equivalent.”? See http://exploredegrees.stanford.edu/schoolofhumanitiesandsciences/physics/#courseinventory . Note that this is not a required prerequisite, so there should be no need to take the actual test if he self-studies some physics mechanics with calculus. (Indeed, it is likely that some concepts in introductory level physics are easier to understand with calculus than without.)
The Physics 5 and former H7 series at UCB does not list anything more than calculus and high school physics as prerequisites for the first course. See http://guide.berkeley.edu/courses/physics/ .
Prerequisites to such a course may include discrete math, abstract algebra, number theory, or CS theory.
Regarding physics for engineers courses, many colleges do not actually have such courses; they just have engineering students take the same courses that physics students take. UCSD is one such school that has a physics for engineers sequence (Physics 2) separate from physics for physics majors (Physics 4). See https://www.ucsd.edu/catalog/courses/PHYS.html .