When I went through Navy Boot in 1964, we had a couple of "cat 4" men in the company. The supposed theory, as explained to us, was this:
If the men could not complete training successfully, they would be discharged honorably (I supposed the technical term would have been "general discharge under honorable conditions). If they completed training, they were to be interviewed and given the option of service or discharge. One, at least, completed boot camp with us; so far as I remember, I didn't learn if he went on to active duty. He came across as a decent young man, but he was obviously below the average range.