The essence of the argument is trivial: one can't send the masses of all monopoles to infinity in the four-dimensional Planck units because the pairs of electromagnetically dual monopoles are inversely related to each other.
There are other ways to show that one can't decouple supergravity from string theory exactly, non-perturbatively. For example, black hole microstates must appear as poles of the scattering amplitudes and their mass (absolute value) starts by something comparable to the Planck mass.
However, I happen to think that this fact doesn't imply that N=8 supergravity can't be perturbatively finite. The supergravity non-stringy calculations should be viewed e.g. as M-theory compactified on the rectangular seven-torus self-dual under the maximum number of U-dualities - which is equivalent to IIB string theory at self-dual radii under T-duality at the self-dual coupling.
You can't decouple SUGRA exactly but it seems plausible that you can decouple it to all orders in perturbation theory.
