  We show that the size of the O(a^2) flavour violating cutoff artifacts that
have been found to affect the value of the neutral pion mass in simulations
with maximally twisted Wilson fermions is controlled by a continuum QCD
quantity that is fairly large and is determined by the dynamical mechanism of
spontaneous chiral symmetry breaking. One can argue that the neutral pion mass
is the only physical quantity blurred by such cutoff effects. O(a^2)
corrections of this kind are also present in standard Wilson fermion
simulations, but they can either affect the determination of the pion mass or
be shifted from the latter to other observables, depending on the way the
critical mass is evaluated.
