Answer

With God’s help,
I find it hard to write at length in English (I manage better with reading). So forgive me for writing in Hebrew. I hope you’ll manage with it.
Let me begin by stating my basic premise: in my view, interpretation has to fit what is written in the text. Someone who “abuses” the text to make it fit some other understanding he has is not being intellectually honest, and it is not right to do that — not with the Torah, not with the Talmud / Talmudic text, and not with any other text. That is why I very much dislike homiletics, because they do not try to interpret the text but rather use it to preach a message whose conclusion is known in advance.
Having said that, I will present a few points that may help you:

1. First, it may be worthwhile for you to read my article on the okimtot (in Hebrew). It deals with a certain aspect of this issue, and I think it offers a pretty good explanation.
2. You assume that the reader always fits the text to his prior assumptions. But in my opinion it is usually the opposite: he tries to fit it to his understanding of what ought to be found in the text itself. That is, from our familiarity with the Talmudic corpus as a whole, we understand the mode of thought, and so when we encounter a text we decipher it both in light of what is written in it and in light of the context (the meaning of the entire Talmudic corpus). That sometimes requires an interpretation that seems a bit out of step with the text. But someone who thinks that the correct interpretation of a text is the simple meaning of the words is mistaken. Reasoning and context always play a part in interpretation, even interpretation along the straightforward reading. For example, when the Torah says that the Holy One, blessed be He, raised His hand, it is clear to us from various sources that He does not have a hand, and so we interpret this metaphorically. If we find in a text a halakhic instruction that contradicts some Talmudic principle, we will interpret it in a way that fits the Talmudic principle.
3. The Mishnah in Avot instructs us to judge our fellow favorably. The commentators on the Mishnah (Maimonides, Rabbenu Yonah) explain that this does not mean some warped interpretation, but rather something required by the context. For example, you see an elderly righteous man chasing a young and beautiful girl down the street with a knife in his hand. If he were a reckless young man, you would say he wants to rape her. But you know him to be a saintly righteous person, and so you interpret the situation differently: she is his housekeeper, who forgot the knife at his house, and he is chasing after her to return it to her. That is a strained interpretation, but the context dictates that it is the correct one.
4. Sometimes the strained interpretation, far from the plain meaning of the text, is in the category of homiletics, and it stands alongside the straightforward interpretation; it is merely added to it, not substituted for it. This is mainly relevant with regard to interpretation of the Written Torah, and less so with regard to a Talmudic text.

 
I read quickly through the link you sent me.
I do not agree with your assumption. It is not true that this is always done. On the contrary, in my opinion these are esoteric examples, and as I wrote to you, you must not take an esoteric example and turn it into a rule. If someone, however important he may be, writes something illogical, then do not accept it. That does not mean that this is the Talmudic method. As is well known, Talmudic study has no problem with dispute. More than that: even if you find such a statement in a certain commentator (like the author of Halikhot Olam that you cited), that is not a law given to Moses at Sinai. You may disagree with him if he does not seem logical to you.
It is true that there is a principle of “we do not multiply disputes” (what you brought from the author of Halikhot Olam, and it appears in other commentators as well), but it is important to understand that this definitely has logic behind it. When two intelligent people who belong to the same school of study, the same discipline, and the same tradition — the tradition of the Oral Torah — disagree with one another, it is more reasonable to minimize the disagreement as much as possible. For example, if you discover that between two amoraim who disagree in a certain case, some analysis yields two separate disputes, you would prefer the analysis that makes it one dispute between them. This is Ockham’s razor: why posit two disputes if there is an explanation that reduces it to one? But of course it only makes sense to do this when the second possibility is reasonably plausible, and when it is plausible that on this particular point no disagreement actually arose between them. Exactly as Ockham’s razor applies only between two theories that both pass the tests of facts and logic. If you have two such theories, you prefer the simpler one. But simplicity in itself does not prove correctness, of course. Quantum theory or relativity are not the simplest theories; Newtonian mechanics is simpler.
I suggest that if you would like to continue the discussion, present one specific example and we can discuss it.