The reason that Moshe and Aharon would be permitted to testify is seemingly because they did not have the halachic status of brothers, not because relatives may testify in this instance. According to the above, however, this is understood, as the reason that the testimony of brothers is permitted is because we do not need the authentic concept of testimony but rather a verification by two trustworthy individuals.
The reason why, in general, converts can say testimony concerning the other, is because the prohibition of relatives saying testimony about each other is not because of a closeness that they may feel for the other person, but, as was explained, is rather only because the Torah decreed as such—not because of a rational reason.
If they are technically not related, they may say testimony concerning the other. The Torah created the concept that “by the mouth of two witnesses...shall the matter be confirmed,” even though it is possible that they may not be telling the truth. The Torah likewise established, that relatives do not have the ability to cause this degree of verification.
However, concerning the testimony of a new month, the focal point of their testimony is not that the “matter shall be confirmed,” but is merely to verify to the courts something that they have already mathematically confirmed. This is not the regular Torah concept of testimony, but rather a clarification of something based on a trustworthy statement that can be verified.
Although Moshe and Aaron may not have had the halachic status of brothers, they still had the natural connection that two brothers have. Therefore, once the verse brought out that we are not worried about a natural affinity, this law applies to all testimony concerning the new moon, (which is not the essential concept of testimony).
The Halacha
The accepted ruling though, is like the contending opinion: that relatives cannot say testimony concerning the sanctification of the new moon.
