  Extended theories are widely used in the literature to describe relativistic
fluids. The motivation for this is mostly due to the causality issues allegedly
present in the first order in the gradients theories. However, the decay of
fluctuations in the system is also at stake when first order theories that
couple heat with acceleration are used. This paper shows that although the
introduction of the Maxwell-Cattaneo equation in the description of a simple
relativistic fluid formally eliminates the generic instabilities identified by
Hiscock and Lindblom in 1985, the hypothesis on the order of magnitude of the
corresponding relaxation term contradicts the basic ordering in Knudsen's
parameter present in the kinetic approach to hydrodynamics. It is shown that
the time derivative, stabilizing term is of second order in such parameter and
thus does not belong to the Navier-Stokes regime where the so-called
instability arises.
