SPOILER US EP 3-09-00

I think the rule probably is that comprehensive, perhaps for the reason you suppose. The fact that they once had a teacher-student relationship makes it likely that Ross would have some chance to influence her chances of getting research grants or fellowships or various other types of things. It probably wouldn't have an effect on her graduating, though anything's possible. But Ross likely teaches in the department that she is studying in, and if her field of study involves a final comprehensive exam or thesis, he might be on the committee that grades her on it.

I had the impression that neither one of them actually knew at first who or what was responsible for the fire.

Right, but by the time this incident with Joey occurred, they had been informed by a fireman that the fire was started by Rachel's hair straightener. That's why Phoebe had moved into Monica's apartment.

I don't remember that part, but I'm not remembering episodes that well these days, so I'll take your word for it.

In that case, I recall someone around here claiming that Rachel's good relationship with Phoebe showed how much she has matured or some such thing. As I recall, I had severe doubts. Now I see they were well founded.