The primary reason you cannot use hardwood as a subfloor for stone tile installations is because there is too much deflection, or flexibility, in the hardwood floor. Not only can it move horizontally between each individual piece, but the pieces also expand and move upwards and downwards. Seasonal movement will cause the wood to swell and shrink, and the stone tile needs to be able to withstand that movement along with foot traffic without flexing too much.
The appropriate thickness of subfloor for stone tile installations is a minimum of two sheets of three-quarter inch exterior-grade plywood stacked on top of each other and screwed and glued into place. The only way to ensure that your stone tile installation will last is to completely lock down the hardwood floor with a sheet of plywood glued and screwed onto the surface, with another layer of plywood on top of the first.
Stone tile installations need a layer of underlayment on top of the subfloor to create a cementitious surface for the thinset mortar to bond with. Underlayments do not add anything to the overall structural integrity or strength of the installation. Rather, they simply give a bonding surface for the mortar, and when adhered and screwed or nailed on top of the two layers of subfloor sheeting, create the only rated and approved installation surface for stone tiles.
The worst type of hardwood floor you can try to install stone tile on top of is a floating floor. Floating floors are not nailed down to their subfloor, which means they are exactly what their name suggests. Before any new subfloor layers can be added to prep for the tile installation, the hardwood needs to be nailed into place so movement is removed from the equation.