For pizza, I use Rose’s method of pre-baking the crust (no toppings), being careful not to oil the bottom of the crust. I let the shaped dough rise on parchment, then slide the parchment directly onto the stone (no pan), then after 1-2 minutes (just enough to set/solidify the crust), I slide out the parchment and continue baking the crust directly on the stone for another 3-4 minutes. When I pull them out I check the bottom to see that they are lightly browned and crispy.
After that pre-baking, though, I never put them directly on the stone with toppings. They go back on the parchment and then onto a sheet pan for the final bake.
I do the same with bread that calls for baking on a stone- rise and start baking on the parchment, then finish it on the bare stone. Or if I’m busy with other things (like dinner), I’ll just leave it on the parchment, it still comes out pretty crispy and browned from the direct heat of the stone.
A large part of the effect of the stone comes from the faster transfer of heat that the solid stone provides. The bottom cooks faster and to a higher temperature than the part of the bread that is only exposed to air. Also, I think parchment is somewhat porous, so it still allows a little moisture to escape.