I'm with Jay J simply because I don't like the idea of layers and layers of old flooring under my new floor. Somebody is going to have to remove it sooner or later.
Asbestos is most dangerous when its airborne. I say wear a dust mask and mist the floor down with a little water to help keep the dust down while you are tearing it up.
For the EPA's point of view....:
© 2017 Renovate Your World LLC