Yibum and Chalitzah: stringency or leniency?

Question

In Yevamoth 8a, we discuss a group of women (enumerated in mishna 1:1) with whom neither yibum (levirate marriage) nor chalitzah (the rejection of levirate marriage) takes place.

According to the gemara, there are two places in Torah whence we can learn about levirate marriage: a man's brother's wife and a man's wife's sister. The former is a situation in which a man A performs either yibum or chalitzah with his brother B's wife when B dies without children (where normally a man's brother's wife is forbidden to him); the latter is that a man may not perform yibum or chalitzah with the sister of his wife.

Up to this point, the gemara has compared the group of women (enumerated in the first mishna) with a man's wife's sister (and hence they are exempt from yibum and chalitzah). The gemara now asks why we don't compare this group to a man's brother's wife, and hence permit yibum and chalitzah with them. The first answer given reads as follows.

אמר ליה רב אחא מדפתי לרבינא מכדי כל עריות איכא לאקושינהו לאשת אח ואיכא לאקושינהו לאחות אשה מאי חזית דאקשת לאחות אשה אקשינהו לאשת אח איבעית אימא לקולא וחומרא לחומרא מקשינן

Said R. Aha of Difti to Rabina: Consider! All forbidden relatives might be compared to a brother's wife and might equally be compared to a wife's sister, what reason do you see for comparing them to a wife's sister? Compare them rather to a brother's wife! — If you wish I might say: When a comparison may be made for increasing as well as for decreasing restrictions, that for increasing restrictions must be preferred. [translation from here]

The gemara answers that permitting yibum would be a leniency, since we would be permitting a marriage where normally (outside of a yibum situation) it would be forbidden. The gemara asserts that we prefer not to do that if there is a stringency that could be applied instead.

My question: is this stringency not a stringency that might lead to a leniency (חומרא דאתי לידי קולא)? Should we not also require chalitzah as a stringency before the woman marries someone else?

Consider, for example, the case of two brothers A and B, where A is married to X, and B is married to Y, who is X's mother. Say that B dies without children, and Y comes to A for either yibum or chalitzah. The gemara says that as a stringency, we do not allow A to perform yibum or chalitzah with Y. However, Y is now allowed to go marry C, another man who is not forbidden to her. If we really should have compared the group of women to a man's brother's wife and not to a man's wife's sister, do we not now have a situation where Y and C might be in an adulterous relationship, as Y wasn't properly cleared from her previous marriage to B?

---

Note: Many of the unqualified statements in this question should be qualified, but for the sake of trimming an already long question, I left out the qualifications.

Answer 1

As suggested in one of the comments, the Gemara is describing an exegetical rule, rather than a principle of erring to the side of stringency when in doubt. This understanding is supported by the gemara's alternative answer there:

איבעית אימא הכא תרי איסורי והכא תרי איסורי ותרי מתרי ילפינן אבל הכא חדא איסורא ותרי מחדא לא ילפינן

If you prefer, however, I might say: In the former cases there are two prohibitions in the one as well as in the other, and a double prohibition may justly be inferred from a double prohibition; in the latter case, however, only one prohibition is involved, and a double prohibition may not be inferred from a single one.

This answer is clearly a rule that is used by an ambiguous hekesh, and presumably these 2 answers are not miles apart.

It is possible that the source for this rule is the principle that when in doubt we follow the stringent ruling, but once written in the "Drasha rule book," it is simply a guideline for figuring out what the pasuk is teaching us.