Funny to me that 2 years ago when I joined this board I mentioned something about Counterparts and a grunge/alternative influence and was laughed out of the building; now we've got a fair number agreeing that "Stick It Out" is faulted for being "too grunge."
I for one can hear those influences on Counterparts and T4E in various places. I love "Stick It Out." So heavy, so power! Cool story, bros: my uncle is the kind of Rush purist who will never admit that any of their songs are the least bit imperfect. He claims to love all their albums equally. He gave me shit b/c I wrote an Amazon review declaring Counterparts my favorite Rush record. Finally, after like 3 hours of arguing, he admitted "Stick It Out" was a lesser favorite because of the grunge/alternative element.
Besides the name-dropping Ytse alluded to, Alex and Geddy also betray their affinity for certain alt rock/grunge musicians in their solo albums. Les Claypool played on a Victor track and Edwin from I Mother Earth was the album's lead vocalist. Geddy had Matt Cameron (Soundgarden, Pearl Jam) play drums on MFH.
Maybe I'm wrong, but it seems like some fans feel it is blasphemous to admit Rush was influenced by alternative/grunge music. Yet it's fine to admit their musical influences in other periods. Oh well, whatevs...