Metal lathe is not applied directly against the substrate.
Hopefully there is an air gap behind the plywood also, and not just 1/16" lol. (plywood 14%+ moisture expands and is subject to accelerated decay)
Expanded metal lathe of the proper wt. can be applied directly, that will be determined by the specific gravity of the stone and its friction coefficient (wire holding), Hopefully a modified mortar/thinset was used to plaster the stone to the lathe.
The thiner the veneer, the more susceptible it is to movement ie. expansive forces.
Also, the average holding ability of staples is less than most other fasteners + staples deteriorate faster than any other fastener in most instances. Thats why in many states, localities ect. they are illegal in many construction methods.