Most of the aesthetic fellowships (and craniofacial fellowships) are unaccredited by the ACGME. Being ACGME approved means that there are rules governing the training (such as call, work hours, number of cases, etc.) the same as residency. It doesn't mean that the fellowships are inferior but you do have to be careful.
The aesthetic fellowship with Dr. Aston at MEETH is a great place and the fellows have a great deal of autonomy. At others, you might find yourself taking all of your attendings call, observing cases and not operating much. And, as pointed out earlier, these fellowships (ACGME or not) should not be confused with those offered by the "board" of cosmetic surgery.