The gemara asks about a case where kiddushin is done in the presence of only one witness, but both he and she admit to the kiddushin. Rashi seems to understand that the question is whether we require eidei kiyum to create the chalos kiddushin or do they only serve as eidei birur just to clarify that it was done. However, further on in Rashi (d.h. v'i leka) he implies that the gemara knew that at least one witness is necessary to create the kiddushin. By simply having him and her admit to being married the gemara understood all along that there would not be any chalos kiddushin. The only question is that maybe a single witness is sufficient to create the status of kiddushin (just as he can be mechayev a shavua) and the admission of the husband and wife is sufficient to confirm that they were married in the presence of a witness.
The gemara concludes that without the presence of 2 witnesses there is no chalos of kiddushin at all. Yet, by monetary issues the gemara 65b concludes that witnesses only serve the purpose of preventing the parties from denying. The Ketzos Hachoshen 241:1 raises a major question: How can monetary issues serve as the source to require 2 eidim for the chalos of kiddushin? How can we learn from monetary issues where eidim are only l'vrurei, that by gittin and kiddushin we need eidim l'kiyumei?
The Ketzos explains that really by monetary issues we also require eidim to make the chalos of the kinyan. Just that in dinei mamonos we have a concept of hoda'as ba'al din, so that the people involved in the kinyan will always serve as "100 witnesses" to make the kinyan go into effect. Since gittin and kiddushin are consisered a chov for others, so that we cannot use the concept of hoda'as ba'al din, we require actual witnesses to make the kinyan go into effect.