As far as the actual halacha:
Syag:
But I will be sure to let the Rav know that he made a mistake about the coffee and grounds being a mixture.
You could let him know that if his sevara is based on the Chazon Ish in O.C. 53, who says this about sand which accumulated in a filter through which mostly clean water is being poured, there are two distinctions:
1)The CH”I states that the sand doesn’t move (because of it’s weight) which is visibly not true with coffee, in which you can see the coffee grounds floating in the water accumulating atop the grounds.
2)That’s not considered a mixture because you have no interest in the water touching the sand, but that’s not the case with the coffee; you obviously need that contact for the coffee’s flavor to be infused into the water. Ayil Meshulash,in 4-40-(111), makes this distinction (he is referring to a case where there are tea leves in a filter, through which water is being poured). Also in 4-7-(19), Ayil Meshulash (in the name of R’ Nissim Karelitz) rejects the notion that the water in the wine sediments (which, as HWGA said, would have been the source for a heter) is not a mixture, based on a clear diyuk from the Chazon Ish and Mishna Berurah.
I’m not trying to cast aspersions on the posek with whom you consulted. Maybe I’m wrong (although I’m pretty sure I read the Ayil Meshulash correctly), and maybe you misunderstood him.
HWGA:
Haven’t you learned mishnayos in your life?
The second mishna in the 20th chapter of mesechta shabbos, which is on 139b, clearly states that this is muttar.
You would have served your cause better to quote the Shulchan Aruch (319 – 9), because the Ran and others learn differently than Rash”i, and the Shevisas HaShabbos (as quoted by Ayil Meshulash; I didn’t see SH”HSH inside) says that it’s because they hold there are borer issues in that case.
Despite the fact that the S.A. paskens like Rash”i, in this case, I believe there would still be a problem of borer.The coffee holds back the water for a little while, and I don’t think we can view the entire process, from the pouring of the water over the grounds through it’s exiting with the coffee flavor absorbed in it, as one action without the tachlis of borer. In the case of the wine sediments, we are viewing it as one complete process. See Ayil Meshulash, 9 – 6 – (21) (he doesn’t make this distinction explicitly, because he’s not discussing coffee).