  Breitenlohner, Maison and Gibbons claimed some time ago that all bona-fide
four dimensional asymptotically flat non-degenerate black holes are in a
symmetry orbit of the Schwarzschild/Kerr black hole in a large set of theories
of gravity and matter. Their argument involved reducing the theory on a
time-like Killing vector field and analysing the resulting three dimensional
sigma model of maps to a symmetric space $G/H$. In the construction of their
proof, they conjectured the existence of a suitable $H$-transformation that
always remove the electromagnetic charges of the four dimensional black hole
solution. We show in this short note that such a transformation does not exist
in general, and discuss a set of boundary conditions on the horizon for the
scalar fields in the sigma model that yield black holes for which the result by
Breitenlohner, Maison and Gibbons can be applied.
