I agree with you about kT and E part you say but I don't agree with that "garden variety kinetic pressure" part. Quantum states for stable configuration are determined by potential well, not simply volume. Another thing is that interacting particle changes it's quantum state. If there are no available quantum states that it can occupy after interaction it can't participate in interaction. And how can we talk about kinetic pressure without interactions between particles?It's just garden variety kinetic pressure if you know E and V, it makes no difference to P what the spin statistics are, or even if the particles are distinguishable or not.