The process you describe is an exceedingly common method of proving a point when there is not factually analogous precedent for that particular point. By way of over-simplified example, there may be precedent for the proposition 1 + 2 = 3, but there may not be equivalent precedent for the proposition that 6 - 4 = 2. An advocate might cite the former to support the latter, even though they are not entirely analogous. In the world of legal citation, this type of citation is usually indicated with cf.
Similarly, there may be a principle of law that is announced in a case that "goes the wrong way" that is nonetheless helpful to support the case of the person who, in this case is on the opposite side. So, again, in an over-simplified example, a court might announce that "the sky is green," and conclude that under the facts of the particular case, a particular result is warranted. Someone on the other side of the same issue might nonetheless argue that this case supports their position, based upon the facts of their case, citing to the conclusion that the sky is green.
This type of argument is much more effective when the opinion announcing the proposition is of significant precedential value -- e.g., an announcement of legal principles by a higher (or highest) court.