Actually, MIT does have ABET accreditation in CS, as does the EECS major at Berkeley, but Stanford, CMU, and the L&S CS major at Berkeley do not. However, per se, it is only really relevant to the patent exam, although students in non-ABET-accredited CS majors can take additional physics or chemistry courses to meet the patent exam requirements. Otherwise, ABET accreditation just indicates that the CS major is of decent or better quality, but non-ABET-accredited CS majors can also be of decent or better quality (but also can be of poor quality). ABET accreditation criteria for CS does include some non-CS science courses.
UCF probably weeds out students with the exam for capacity reasons (i.e. it probably cannot handle all of the students who want to major in CS and get C or higher grades in the prerequisite courses). Most other schools that do this use grades or GPA in prerequisite courses as the primary means of admission to the major; UCF is unusual in having a high stakes exam for this purpose.