Question

As a rule, a migo is built on the fact that the claimant could have made a different, better claim, and therefore he is believed even regarding the present, weaker claim.
Therefore, it is clear that one cannot invoke a migo if the claimant could not really have made the other claim, for example if it is a claim that requires brazenness (and therefore someone who admits part of a claim is not exempt on the basis of a migo that he could have denied the whole thing, because a person is not brazen enough to deny his creditor outright).
My question is about the present claim he is making, not the alternative claim. Here, seemingly, it should make no difference at all what he is claiming and how far-fetched/problematic the present claim is, since his credibility comes from the fact that he could have made a different claim. And yet the Talmud says that if the present claim makes the claimant into a wicked person, he will not be believed even if he has a migo (for example, Babylonian Talmud, Ketubot 18b: “This is indeed our handwriting, but we were coerced because of money”). Why is that? Why is it relevant that his present claim is illegitimate because he is making himself into a wicked person, if the credibility is based on his ability to make the other, better claim?