I suspect that http://arxiv.org/abs/astro-ph/0404111
is somewhat responsible ;) .
Below is my reasoning (but please let me know if you think otherwhise).
By changing the value of G on all scales a(t) will consequently change and, when looking at linear theory scales, the effect on the power spectrum will be an overall amplitude change. This conclusion is based on the observation that LSS power spectrum alone- 0.04>k>0.1 1/(Mpc/h) say- is sensitive to n and amplitude, in the sense that a change in other cosmological parameters, say, omegam for example, is mostly degenerate with a change in n and/or amplitude. Of course the use of additional information encoded in the redshift space distortions, non-linearities, higher-orders correlations etc. may-and probably will- enable us to break this degeneracy. But let us deal with LSS linear power spectrum alone and assume n and amplitude are being suitably marginalized over.
So if one changes the value of G only on large scales, something similar should happen except that now also the power spectrum *shape* gets modified because of the behaviour of gravity in the "transition" between G and G_N.
As long as one marginalizes over amplitude and a reasonnable range of n and uses the information in the linear power spectrum *shape* it should be ok. It is true that the P(k) shape modification might somewhat depend on the details of a(t), but that effect is small (we tested that- and this is somewhat related to their criticism to 0404111) . And anyway, since one is doing a null test, these kind of approximations affect (only mildly) the size of the errors not the central recovered value.
The problem with modifying the 1/r^2 behaviour at small scales is that there would not be stable orbits (and I am sure we would not like this to happen...)
But I agree, if we could measure cosmological parameters (say omega_m) using obseravtions that rely on physics at different scales, and get the same answer, then a strange behaviour of G can be ruled out (or constrained)
Having said all this, I see that astro-ph/0501366
paper does not marginalize over n, includes non-linear scales, but does not include redshift space distortions...
On the other hand that particular model for modification of Newton's law is not the only one one can think of...
In summary, given the large theoretical uncertainties involved, I think that these determinations (both astroph 0404111 and 0501366) should be considered more like "an order of magnitude" constraint, which given the state of affair before april 2004 (no constraint at all) is still useful.
I hope this helps, and I'll be happy to hear your views.