The gemara is clear that we only believe an individual witness for issurim when there isn't a chezkas issur. Rashi and Tosafos explain based on the gemara in yevamos that although we do believe an eid echad for shechita even though there is a chezkas issur, that it is because it is completely in his control to rectify the situation. Tosafos explains that not only if it still is in his hand, but even by shechita where right now it can't be fixed but since it was in his hand originally, an eid echad is believed.
Rashi at the beginning of the 10th perek of Yevamos implies that the source for eid echad being believed is a sevara, because otherwise people could never eat in each others home, which is assumed to be not possible. Tosafos however writes that it is learned from Nidah who is believed on her tahara. Tosafos therefore asks, if we learn from Nidah then we should even believe her when there is a chezkas issur? Tosafos answers (based on maharsha) that regarding the tu'mah that results from the actual bleeding, that is not regarded as chezkas issur since there is no chazaka that she will continue bleeding past the 7 days, and in regard to the aspect that once she has been tamei she remains tamei until immersing in a mikvah on which there is certainly a chezkas issur, that is in her hands to control since she can now immerse. Therefore, it conforms to the rules that an eid echas is only believed if there isn't a chezkas issur or it is in his control.
The Ramban offers another answer: Since she is believed for herself, she is believed for her husband. The Maharatz Chiyus says that the Chasam sofer explains the Ramban to mean that since she established her status of Nidah, she is believed to say that it has been removed. But he points out that it doesn't fit with the Ramban since the Ramban says explicitly that she is believed even if the husband knew on his own that she is a Nidah. The M.C. therefore explains based on a principal that if one knows the chazaka to be wrong, he is not bound by it. Since she knows that the chezkas issur is wrong because she is now tahor, she is not bound by the chezkas issur. Now, once she is believed to prevent herself for receiving malkus for having relations with her husband, she is believed to prevent him from malkus as well.
Another answer of the Ramban is that it is a gezeiras hakasuv that she is believed without eidim since it is impossible to have eidim on this. However, this answer will only work with Rashi because based on this, Nidah certainly will not be able to serve as the source for the concept.
The final answer of the Ramban sounds like Tosafos, but is really different. The Ramban says that since it is in her hand to change her state at some point in the future by counting and going to the mikvah, she is believed. The difference between the Ramban and Tosafos is that according to Tosafos the fact that the bleeding will stop makes it no longer a chezkas issur, but according to the Ramban it is still a chezkas issur just that eventually it will be in her hand to become tahor. The Steipler points out that according to Tosafos, we cannot prove that a chazaka that is going to change such as the bleeding retains power of chazaka, because tosafos says that it will not be considered a chezkas issur. But according to the Ramban we can prove that even if the chazaka will change it is considered a chazaka because here also we consider it a chezkas issur, just that it is in her hands.