It strikes me as something that may be misremembered though, which makes it harder to find. Not that it didn't necessarily happen, but that some details changed over the years and it's being told differently than it happened. Without better sources it's hard to know how much changed in retelling, but there's a couple points that strike me as definitely modified

Elder Oaks was a justice of the Utah Supreme Court starting in 1980 so wouldn't be making legal arguments at that point. Maybe earlier, in the 70s, when he was president of BYU? That would obviously be less in his role as a lawyer and more as the president of BYU, but would fit well.

Also, Stanford, as a university, would have no standing to sue BYU for their housing policies, so that part doesn't make sense either. Maybe someone from Stanford was the lawyer for a BYU student (who would have standing)?

In any case, I can find zero record of this and would love to read up on it, so if you have any additional info that would help me find it, I'd appreciate it.