From what the Bridgestone piece says, it doesn't seem like they are recommending putting anything down between the tires and concrete.
"Concrete is not the tire enemy some people think it is.
We would recommend the following steps in storing a vehicle:
1. Make sure the floor / ground surface is free of any petroleum product contamination (Oil, grease, fuel, etc.) since petroleum products will attack rubber and can cause significant damage to compound characteristics.
"3. Place a barrier such as plastic, cardboard, or plywood between the tires and the ground surface."
Notice in note #1 they specify "floor/ground", but when they talk about putting a barrier down, they only talk about "the ground".
You are correct that it appears pretty clear.
But many shop concrete floors are oily, and that would definitely require something to protect the tires.
I could eat of my shop floor, so I think I will be ok!