Nearly all HYPSM… type private colleges have a variety of different math starting points and tracks with different levels of rigor, use of proofs, use of Matlab and other engineering tools, etc. Such colleges typically give all freshman a math placement test to help decide which math starting point is the best option. They also often have placement advisers that consider best placement at a more holistic level, beyond just placement and AP scores… consider the goals of the individual student and planned field of study, how confident they are about their math ability, etc.
However, the use of placement tests does not mean students who take MV calc or linear algebra taken in HS always skip over the material in college. As noted earlier in the thread, in many cases, colleges recommend that students repeat the material in one of the more rigorous track options, such as repeating the class with greater rigor and more use of proofs than occurs in the standard track. Some colleges also make it fairly easy for students who want to skip over the material and not repeat to do so. I skipped over such classes in college. I knew a kid from the neighboring dorm who started out in grad math classes.