I'm not familiar with your soil and freeze/thaw, moisture or expansive soil conditions. but in looking at historical data for your area, you do have occasional freezing conditions and seasonal rain which needs some attention. The bottom of footings need to below grade to help offset those situations. The compacted fill allows for drainage and to help offset irregularities in soil conditions. It is cheap insurance, because someone may have buried a cactus or log under your slab.
Post tensioning of the slab is great, but a dumb slab with adequate fiber and mesh reinforcing is probably adequate. A 6" thick slab should be an absolute minimum.