I have never much liked mesh or light reinforcing for slabs because even despite careful chairing prior to the pour, as a concrete hose is dragged over the reinforcing, or the team of concrete placers marches over it, it usually ends up down in the sand layer, or worse yet part down in the sand, and the opposite side pivoting over the chair ends up poking through the top surface. On that note, mesh does have a slight advantage because it can more easily be re-lifted just as the concrete placement approaches.
Now my experience is more on industrial or commercial projects requiring heavy duty floor performance where it was quite reasonable to use fairly heavy reinforcing that can support construction loads (#5s or 15M bars minimum). This is of course not reasonable for the application in question here.
As far as the need for reinforcement, I would suspect that unless the floor is acting as a diaphragm that there would be no code requirement for reinforcing (but I am not familiar with California Seismic requirements). If you read slab-on-grade literature from PCA, with proper joint control there is no real need for reinforcing steel, although it does have the added advantage of providing some bridging strength over small voids cause by soft spots or poorly compacted backfill over utilities or near foundations. The primary reason for reinforcing steel is to provide crack control for shrinkage/creep, particularly if jointing &/or mix design &/or installtion quality is not well controlled, but then only if it is installed in the proper location (i.e. mid slab for a single layer, within proper cover distances for top & bottom steel).
An alternate that you might want to consider is fibre reinforcement (but because of the exposed nature of the surface, use polypropylene rather than steel fibres). And like any specialty product, the contractor should be familiar with its use. Most suppliers that I have dealt with are willing to provide a manufacturer's rep to assist the contractor in proper use of their product.
Hope this helps...