Toi might actually be incorrect. It is a Svara. The reason the Torah has to say it, says Tosafos in Nidah 46b, is for the concept of Kiyum — that once he says he accepts it, he can’t nullify it anymore.
Another reason, suggests Tosafos, is that it is really the other way around: Since the Torah says that he can nullify it, therefore she is Noderes AL Daas Baalah. Once this Svara — which is based on the Pasuk — exists, it extends farther than the original Halacha. Even if the marriage is not Mide’oraisa, once she thinks the Halacha applies, it applies.