  We reconsider the widely held view that the Mannheim--Kazanas (MK) vacuum
solution for a static, spherically-symmetric system in conformal gravity (CG)
predicts flat rotation curves, such as those observed in galaxies, without the
need for dark matter. The conformal equivalence of the MK and
Schwarzschild--de-Sitter (SdS) metrics, where the latter does not predict flat
rotation curves, raises concerns that the prediction in the MK frame may be a
gauge artefact. This ambiguity arises from assuming that, in each frame, test
particles have fixed rest mass and follow timelike geodesics, which are not
conformally invariant. The mass of such particles must instead be generated
dynamically through interaction with a scalar field, the energy-momentum of
which means that the spacetime outside a static, spherically-symmetric matter
distribution in CG is, in general, not given by the MK vacuum solution. A
unique solution does exist, however, for which the scalar field energy-momentum
vanishes and the metric retains the MK form. Nonetheless, we show that in both
the Einstein and MK frames of this solution, in which the scalar field is
constant or radially-dependent, respectively, massive particles follow timelike
geodesics of the SdS metric, thereby resolving the apparent frame dependence of
physical predictions and unambiguously yielding rotation curves with no flat
region. We further find that the general form of the conformal transformation
linking the Einstein and MK frames is unique in preserving the structure of any
diagonal static, spherically-symmetric metric with a radial coefficient that is
(minus) the reciprocal of its temporal one. We also comment briefly on how our
analysis resolves the long-standing uncertainty regarding gravitational lensing
in the MK metric. (Abridged)
