My question is basically the same as this commentor. Is this a denial of the principle of Grama as a leniency (as R. Belsky alludes to in the footnote, arguably) or is there something specific about the switch and its intended use which is different than the Tzomet switches?
Rav Belsky, z"l, explicitly declares his reasoning in the letter:
...a tiny possibility of ספק is introduced so that the odds of the melocho being completed is reduced somewhat or delayed minimally. This concept has no place in Halacha.
My understanding is that his reasoning is not that different from the general principle that we are not concerned with the kashrus of microscopic organism. Something has to be distinct to be halachically significant. Furthermore, the explicit intention of the user is to accomplish the end result. The negligible micro-process is halachically insignificant. Real grama involves real uncertainties and/or distinct delays. According to the kosher-switch makers one should be allowed to keep striking a match until it lit because each time there is an uncertainty if it will light. If they altered it such that one wouldn't know if even repeated tries would result in it working at all, all Shabbos, and that, even if it did, it wouldn't be for at least minutes or hours after the action, perhaps then Rav Belsky would be lenient, in those situations in which we are lenient regarding grama. (As Rav Belsky mentions, this switch, according to its makers, should ultimately do away with all the 39 melochos.)
As an aside, I believe Rav Nachum Rabinovitch, shlit"a, also employs a similar reasoning in arguing against grama machines. Ironically, the Kosher Switch-makers try to use him as if he endorsed their product, which is particularly egregious since my understanding is that he was eventually forced to explicitly write them otherwise.
Finally, the reasoning behind the ban is even more explicit here: http://matzav.com/gedolim-kosher-switch-should-not-be-brought-into-the-jewish-home
He also signed on this letter, which allows for grama devices in hospitals.