Yes, which is why I noted a page earlier that no one had mentioned the erector spinae and that it cannot be neglected if you wish to achieve a strong core, preserve muscle balance, and prevent injury. A proper abdominal routine requires core specific exercises for both the frontal and posterior core. High level athletes are put through a vigorous core (abdominals, obliques, and erectors) regiment that mirror the required movements in their given sport.
Right, I don't see any disagreement there, do you?
Did I say supplementary? No, I said complimentary, and integral to strength training. In essence, just as you shouldn't strengthen your upper body and neglect your lower body, you shouldn't neglect core specific training. As high level athletes enter the final periodized stages of conditioning, they do not cut back or stop core-specific training. Instead core-specific training continues to increase in volume and intensity in step with the rest of their resistance training program.
Besides the last sentence, you could say it's a matter of semantics. Core training increases because weight loads increase as the person gets stronger. Ab work is supplementary/complimentary which is why it's always done last. The types of exercises and workouts listed in this thread to the OP seem like entire days dedicated to the abs.