I don’t think it is reasonable to assume that Brisker Rov was not aware of the Rambam, unless it was in some obscure Arabic letter from a Genizah.
Furthermore, in the relationship of old texts, I think we hold opposite: if we discover a new text by a Rishon, or by Rabbi Akiva, or by Melech Shlomo, this will not have a definite effect on halakha: one of the reasons we follow a Rishon because it was scrutinized by later generations.
I agree that one should be careful with orally reported opinions. first, they may be incomplete, second, the author did not put it in writing for some reasn, third, related to 2, the author may have intended it to a specific time and person. For example, in this case the Rov is saying it to a Brisker student, so presumably, in his view, the hishtadlus of being a Brisker student is sufficient enough.
I don’t think Rov advocated quitting learning and sitting in a cafe on Ben Yehudah waiting for the shidduch to show up.