Additionally, the Gemara in Yevamos 6a says that the lav of Shabbos is more stringent and perhaps cannot be nidche by an assei. Rashi explains that the reason that the lav of Shabbos is more stringent is because it is comparable to avodah zarah. This Gemara is not only referring to one who desecrates Shabbos in public, but in private as well.
Therefore the logic that Moshe entertained that one who is michallel Shabbos should deserve the same punishment as one who does avodah zarah applies equally to one who does so in public as well as in private. So when Hashem answered that the mekoshesh deserves death by stoning, the same should apply to one who desecrates Shabbos in private – even if the punishment of stoning stems from the avodah zarah aspect of chillul Shabbos.
For questions or comments, e-mail RabbiRFuchs@gmail.com.