  We show assuming small data that massless solutions to the reflection
symmetric Einstein-Vlasov system with Bianchi VII$_0$ symmetry which are not
locally rotational symmetric, can be arbitrarily close to and will remain close
to isotropy as regards {to} the shear. However in general the shear will not
tend to zero and the Hubble normalised Weyl curvature will blow up. This
generalises the work \cite{NHW,WHU}, which considered a non-tilted radiation
fluid to the massless Vlasov case. This represents another example of the fact
that almost Ehlers-Geren-Sachs theorems do not hold in general and that
collisionless matter behaves differently than a perfect fluid.
