To get a better understand of what is going on, take a look at the plot below, also linked here: http://en.wikipedia.org/wiki/File:Dispersion_Relationship.gif
What the author meant by "letting the speed of light go to infinity" is that the we let the slope of the blue line become infinite. In that case, the solid red line would not curve as shown below, but look much more like a step function. This same effect of making the plot look like a step function can also be obtained when we take the asymptotically large value of $k_x$, i.e. if one plots much larger values of $k_x$ below (instead of 0-3, one plots from 0-1000 for instance).
What I am trying to say is that one should not really think of taking the speed to light to be infinite (which is physically unreasonable, of course), but to take the large $k_x$ limit in which you can really think of the surface plasmon polariton as really being solely being comprised of a surface plasmon (i.e. there is no mixing between light and the surface plasmon at these large values of $k_x$.
This is precisely why inelastic electron scattering, which usually has a poor momentum resolution (at least compared to these effects), is unable to probe the surface plasmon polariton limit. It averages over a large portion of the $k_x$ axis above and effectively measures only the surface plasmon. Light, on the other hand, cannot couple the the surface plasmon polariton directly, as it doesn't have enough momentum to transfer to the SPP. Therefore, one has to come up with clever ways, for example making a grating out of the material one wishes to probe, to get light to couple to the SPP.
