The gemara has a machlokes between r' nachman and rav sheishes whether bitul of a gett must be in the presence of 3 dayanim or if it is sufficient to only have 2. On 33a the gemara makes this machlokes dependent on the machlokes r' yochanan and reish lakish why the chachamim decreed against bitul in fron of a beis din. R' Yochanan holds like r' nachman that bitul in the presence of 2 is sufficient which will not be enough for the word to get out that he was mevatel, therefore this process can lead to her thinking she is divorced when she is really married and her children from her new marriage being mamzeirim. This problem would be solved by simply instituting that 3 must be present on the beis din, but Tosafos points out that R' Yochana is also concerned of the aguna problem addressed by reish lakish. Reish lakish holds like r' sheishes that bitul requires 3, therefore she will surely find out that she is not divorced, but chazal wanted to protect her by making it difficult for him to nullify her divorce by forcing him to be mevatel in her presence or the presence of the messenger.
It would seem that the basic machlokes between r' nachman and r' sheishes whether bitul requires 2 or 3 on the beis din, is a machlokes on a d'oraysa level. However, Tosafos (32b) implies that all agree that on a d'oraysa level the husband can be mevatel even without 2 people hearing his bitul (perhaps even without anyone hearing it). The requirements of 2 according to r' nachman and 3 according to r' sheishes are for the concerns that r' yochanan held to be the reason for the decree to prevent this type of bitul, namely, she will be married and think she is divorced and her children will be mamzeirim. It comes out from Tosafos that according to r' nachman, m'doraysa one can be mevatel even without 2, the entire heter to be mevatel in front of 2 was a concern of mamzeirim - Rabban Gamliel held that this was still a concern and would have been mesaken 3 (just as r' sheishes holds that chazal were originally mesaken 3 due to a mamzierim concern), but because of the aguna concern they required notifying the woman or shelaich.
The Ran seems to reject Tosafos assumption and holds that 2 people are necessary to be part of the beis din on a d'oraysa level, because "ein da'var sh'berva pachos mishnayim". It is only R' sheishes who requires 3 for the concern of mamzeirus.