  Non-integrability is often taken as a prerequisite for quantum
thermalization. Still, a generally accepted definition of quantum integrability
is lacking. With the basis in the driven Rabi model we discuss this careless
usage of the term "integrability" in connection to quantum thermalization. The
model would be classified as non-integrable according to the most commonly used
definitions, for example, the only preserved quantity is the total energy.
Despite this fact, a thorough analysis conjectures that the system will not
thermalize. Thus, our findings suggest first of all (i) that care should be
paid when linking non-integrability with thermalization, and secondly (ii) that
the standardly used definitions for quantum integrability are unsatisfactory.
