Your question is in fact a question on the Gemara at end of Shevuos 41b, which the Ketzos cites.

(a) The Gemara there states that Reuven said to Shimon "Return to me the 100 zuz that I lent you". Shimon replied that there had never been such a loan. He then went and brought witnesses that Reuven had lent him the money but that afterwards he repayed. Rava (who the halacha follows) said "Kol Ha-Omer Lo Lovisi k'Omer Lo Porati Dami". Rashi explains that we believe the 2 eidim that Shimon borrowed but we do not believe them that he repayed because the Hoda'as Baal Din of Shimon is worth a 100 witnesses.

(b) Your question is that granted that Shimon's implicit admission that he did not repay is equivalent to eidim on the latter, but against that there are witnesses that he did repay, so this should be considered as 2 against 2 and we should therefore say that since a doubt exists we cannot force to Shimon to pay up because we should say "HaMotzi meChaveiro Olov HaRayah" and Reuven should require a proof to oblige Shimon to return the money?

(c) The Rosh there (6:16) anticipates this question and writes that even though there are witnesses that Shimon repayed, nevertheless Shimon is believed more than the witnesses in order to make himself obliged to pay.

(d) The Ritva explains a little more and writes that it is clear that for the rest of the world the 2 witnesses who testify that Shimon repayed are valid witnesses. However since Shimon admits about himself that he did not repay, this means he is saying that from his point of view the tesimony of the eidim is invalid. Shimon's admission is more powerful than 100 eidim in relation to himself because he is saying that he does not accept these witnesses, so his own admission to make himself pay is stronger than 100 eidim saying that he does not have to pay.

(e) The Perisha on Tur Choshen Mishpat 79:1 DH Hodaas gives a different and ingenious explanation why we do not say Trei Utrei in this Gemara. The Perisha writes that the main reason why Shimon must pay is because his claim that he never borrowed has been contradicted by 2 eidim. However against this one could argue that it does not matter that he has been contradicted because we have 2 eidim that he payed up. The Perisha writes that because he implicitly admits that he did not pay up this is like having 100 eidim that he did not pay against 100 eidim that he did pay. These two sets of 100 eidim therefore cancel each other out and all we are left with is the fact that Shimon is deemed a "Kafran" - somebody who has been disproved - on his claim that there was never a loan. Since Shimon has been disredited it follows that he has to pay up.

(f) The Rema on Shulchan Arukh Choshen Mishpat 79:1 writes that the admission of Shimon is believed more than 100 eidim. It seems to me that this may be consistent with the Rosh and Ritva mentioned above in (b) and (c) who explain why Shimon is believed more than the eidim and not merely equal to them.

[See also SM'A Choshen Mishpat 79:2 by the author of Perisha]

KOL TUV

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