quantum electrodynamics - Can the mass term be responsible for creation and destruction of particles?

In an interacting quantum field theory, for example, QED, the Dirac mass $m\bar{\psi}\psi$ is a piece of the free Dirac Lagrangian. On the other hand, the interaction term $j^\mu A_\mu=e\bar{\psi}\gamma^\mu\psi A_\mu$ is supposed to be solely responsible for creating or destroying a particle or an antiparticle.

However, the answer here by Lubos Motl states

"...the Dirac mass term destroys a particle and creates a new one, or destroys/creates a particle-antiparticle pair, or destroys an anti-particle and creates a new one."

In free theory, the particle number must be conserved. So my question is whether the interpretation of Lubos is valid.