  Garcia and Campuzano claim to have found a previously overlooked family of
stationary and axisymmetric conformally flat spacetimes, contradicting an old
theorem of Collinson. In both these papers it is tacitly assumed that the
isometry group is orthogonally transitive. Under the same assumption, we point
out here that Collinson's result still holds if one demands the existence of an
axis of symmetry on which the axial Killing vector vanishes. On the other hand
if the assumption of orthogonal transitivity is dropped, a wider class of
metrics is allowed and it is possible to find explicit counterexamples to
Collinson's result.
