  Every theory that modifies gravity at cosmological distances and that is not
already ruled out by the Solar system observations must exhibit some nonlinear
mechanism that turns off the modification close to a compact matter source.
Given this nonlinearity, one might expect such a theory to show a large
gravitational backreaction, i.e. an order one influence of the small scale
inhomogeneities on the large scale evolution of the Universe. We argue that
this is not necessarily the case. If the dominant nonlinear terms in the
equations obey a shift symmetry, the averaged effect of the nonlinearities can
be small, although the effect on small scales is large. This happens for DGP
(-like) modifications and so called f(G) (or Gauss-Bonnet) models. For both
type of models the shift symmetry is part of the larger "Galilean" symmetry.
