OPINIONS: The Gemara discusses the law of "Shevu'as Modeh b'Miktzas." When a person admits that he owes a portion of the money claimed by the lender, the Torah requires that he swear that he does not owe the rest of the money. Once he swears, he is believed. The Gemara explains that the borrower is believed in such a case because a borrower does not brazenly deny the claim of his creditor whom he admits lent him some money. Accordingly, the possibility exists that the borrower really did not return any money to the lender. Since the borrower would not be so brazen as to lie and deny the entire debt, it is assumed that he may be stating a partial admission in order to push off the lender and gain more time to pay back the loan. The Torah therefore mandates that he support his claim with an oath that he does not owe any money. (In contrast, when he outright denies having taken a loan in the first place, the Torah does not require that he take an oath.)
What does the Gemara mean when it says that a borrower does not brazenly lie in the face of the person who lent him money?
(a) RASHI in Bava Kama (107a, DH ked'Rabah) explains that the borrower recognizes that the lender did him a favor by lending him money. The borrower's gratitude prevents him from being brazen towards the lender. (The Gemara in Bava Kama (107a) discusses a case in which the opposite is true: when a person entrusted with an object to guard claims that the object was stolen, he must take a Torah oath to this effect (according to Rav Chiya bar Yosef) in order to exempt himself from liability. Since the person with whom the object was entrusted was doing a favor for the owner of the object, he is not beholden to him and has no reservations about being brazen to the owner of the object. He must take an oath because he is suspected of fabricating the claim that the object was stolen.
The TOSFOS HA'ROSH (DH Mipnei) asks that it is apparent from a number of Mishnayos that one is not required to take an oath if he claims that he owes nothing to the person whose object he watched (see Shevuos 42b, 43a, and TOSFOS DH Chazakah), just as one is exempt from an oath in the case of a loan (when he denies everything he is exempt from an oath, and when he admits to part of the loan he must take an oath).
(b) TOSFOS (ibid.) quotes RABEINU TAM who explains that the Gemara's statement that a borrower does not brazenly lie to his creditor means that people in general are reluctant to lie (in front of Beis Din) and entirely deny that an event ever occurred.
(c) TOSFOS (ibid.) quotes the RIVA who explains that a person does not lie so much in front of a person who clearly knows that he is lying. (The Tosfos ha'Rosh seems to combine the explanations of Rabeinu Tam and the Riva into a single explanation.)