The notion that Torah study should be evocative of the experience of receiving the Torah at Mount Sinai is a frequent halakhic and hashkafic theme. The Talmud (Berakhot 22a) teaches that Torah study must be undertaken with a sense of awe and reverence, as that was case at Sinai. Further, we are taught that the “metargem” who participated in the k’riat haTorah may not raise his voice louder than the “korei”, as Moshe’s voice was not raised louder than G-d’s at Sinai (Berakhot 45a). The Tosafot (Chagigah 15a) cite the Talmud Yerushalmi in describing incidents of Torah study in which fire came down from the sky, in imitation of the Sinai experience.
This principle extends to the sefer Torah itself. The Beit Yosef (Y.D. 274) cites the Responsa Ramban as disqualifying a vocalized sefer Torah for that reason. R. Natan Gestetner (Resp. L’Horot Natan, II, 31) explains that it is also for this reason that “every parshah that Moshe Rabbeinu did not divide, we do not divide either (Berakhot 12b).” Our learning (in the form of k’riat haTorah) is to be patterned after the original learning at Sinai. However, R. Gestetner observes, that understanding allows for a chidush: since Moshe actually interrupted not only between parshiyot but between topics as well, we can also separate topics.
Along similar lines, Rav Soloveitchik (as quoted by R. Mordechai Willig, Beit Yosef Shaul, IV, pp. 163-164) explained the requirement for a minyan during k’riat haTorah is not due to the concept of davar sheb’kedushah, but rather to the fact that k’riat haTorah is meant to evoke the original giving of the Torah. As that experience took place in the presence of the entire Jewish people, we require a minyan, to represent the Jewish people.
This would then explain the position of the Rambam (Hil. Tefilah 13:6). The Talmud (Menachot 30b, Bava Batra 16a) states that the last eight verses in the Torah (following the death of Moshe) are distinct from the rest of the Torah, either written by Yehoshua or written by Moshe but not transmitted to the Jewish people along with the rest of the Torah. As a result of this, rules the Talmud, “They are read yachid”. Many theories exist in rishonim as to what this means. According to the Rambam, it means these verses can be read without a minyan. Based on the above, this view can be understood: the minyan represents the Jewish people, to recreate the Sinaitic experience; as these verses were not part of that experience, no minyan is required.