  Observational evidence accumulated over the past decade indicates that
accretion discs in X-ray binaries are viscously stable unless they accrete very
close to the Eddington limit. This is at odds with the most basic standard
accretion disc theory, but could be explained by either having the discs to be
much cooler whereby they are not radiation pressure dominated, or by a more
sophisticated viscosity law. Here we argue that the latter is taking place in
practice, on the basis of a stability analysis that assumes that the
magneto-rotational-instability (MRI) responsible for generating the turbulent
stresses inside the discs is also the source for a magnetically dominated
corona. We show that observations of stable discs in the high/soft states of
black hole binaries, on the one hand, and of the strongly variable microquasar
GRS 1915+105 on the other, can all be explained if the magnetic turbulent
stresses inside the disc scale proportionally to the geometric mean of gas and
total pressure with a constant of proportionality (viscosity parameter) having
a value of a few times 10^{-2}. Implications for bright AGN are also briefly
discussed
