The presumption that “a person does not brazenly deny it to his face” (Nedarim 91a) — what is its basis?
Seclusion? connection? levirate bond? and then also in the case of a yevamah…
Or betrothal?

By the way, I saw that at the end of the booklet on migo you wrote, “This booklet was presented before several of the great sages of the generation.”
We would be happy to receive email addresses, if you have any, of the leading sages of the generation…

That booklet was published by friends from Bnei Brak who took part in a class I gave there to yeshiva students and kollel members many years ago.
They are responsible for what is written there, and they are the ones who passed the booklet around in order to receive critiques. I have no idea to whom, or how great he is. The one whose remarks appear at the end together with my responses is Rabbi Yosel Schreiber.

As for your question,
From the Talmud itself, the matter is not explicit. The wording is that she does not brazenly deny it to her husband’s face, but they connect this to the fact that he himself knows. Where he does not know, she does brazenly deny it. Simply put, the explanation is that the brazenness is only in lying when he knows.
In principle, there is no general presumption that a person does not brazenly deny something to another person’s face. It is said here only regarding a husband.
Something similar appears in the idea that a person does not brazenly deny a creditor to his face. It is the same reasoning, for different reasons. In the case of a creditor, he did him a favor, and in the case of a husband we can ask whether it is because she needs him, or loves him, or fears him.
However, in Bava Kamma 107a, Rashi and Tosafot disagree regarding the presumption that one does not brazenly deny it: whether this applies only to a loan or also to a deposit. According to Rashi it applies only to a loan, which implies that it depends on the fact that he did him a favor. But in the case of a deposit, where he did him no favor, he certainly would brazenly deny it. But according to Tosafot there, the presumption that one does not brazenly deny it applies also to a deposit, which implies that a person does not brazenly lie to the face of someone who knows the truth even if that person did him no favor. According to that, in our case as well there is no need for him to be her husband — neither by marriage nor by betrothal; it is enough that he knows the truth. The reason they spoke of her husband is that this is what the Talmudic passage is discussing, but there is no need for him actually to be her husband.
However, according to Rashi, who holds that the presumption applies only to a loan, it seems that there is no such presumption regarding just anyone, even if he knows the truth, and we need some reason to establish that she would not brazenly deny it. And the reason is that he is her husband. Now one must consider the reason for this, and from that we can learn whether it applies also to a yevamah, or a betrothed woman, and the like. If it is because she fears him, then perhaps only in the case of a married woman. If it is because of affection for him, then perhaps also in the case of a betrothed woman.
The reason is not explained in the Talmud, and I have not looked into the commentators on this just now.
But in practical Jewish law, none of this makes much difference, because in any case one must assess whether this is in fact a situation in which the woman would not brazenly deny it, or would. That depends on changing circumstances and accepted social norms. It is already stated in the Shulchan Arukh (in the name of the Ran) that in an insolent generation we do suspect that she would brazenly lie. Therefore there is little point in discussing whether this was said about a married woman, or a betrothed woman, or a yevamah. In any actual case that comes before us, we will in any event have to judge it on its own merits and not by the rules stated in the Talmud.
I then saw that in Tosafot, s.v. “The Presumption,” Ketubot 18a, it says explicitly that there is a connection between these presumptions (brazenness toward a creditor and the brazenness of a woman), and according to Tosafot’s approach it should be explained as I wrote above.