Question

The Rabbi always argues that halakhic ruling should come from the first order, meaning from analysis of the Talmudic passage and the different approaches, out of which the halakhic decisor arrives at the law. Second-order ruling—meaning a technical ruling based on counting medieval authorities (Rishonim) or discussing the approaches presented in the Shulchan Arukh—is presented by the Rabbi as not correct from a Torah perspective. If I understand the Rabbi correctly, the halakhic decisor should arrive at the halakhic truth and not at a formal result that stems from non-essential factors. Sometimes there are rules of thumb—Rabbi Yosei always has his reasoning with him, the law follows Shmuel in monetary matters, and the like—but even these are apparently based on first-order principles of ruling. 
But when one studies the sources, a different approach seems to emerge. The rule "when the many disagree with the individual, the law follows the many" appears to be a procedural rule. Since there is agreement among the majority, the law follows them whether or not you think the truth is with the individual. Akavya ben Mahalalel says this almost explicitly when he tells his son to follow the majority and not him, since he is in the minority. The second reason the Mishnah gives for mentioning the opinion of the individual—so that one may rely on it in pressing circumstances—also seems to offer a non-essential rationale. If the individual is mistaken, why may one rely on him in pressing circumstances? Either way, either the law should follow him, or even in pressing circumstances one should not be able to rely on him. It would seem that the Talmud assumes there is truth in both approaches ("like a hammer that shatters a rock," as Rashi describes it), and halakhic ruling is not only a substantive matter but also a technical one. If there is a majority of opinions, one follows the majority. If there are pressing circumstances, one follows the individual, and so on. The substantive rationale does not always decide the matter. Does the Rabbi agree with this argument, or do you have another explanation for second-order ruling of the kind I described here?