You're spot on. I'm fortunate -- despite my not being world-class I share solos with the guitarist around 50/50. Mine are mostly an even split of piano, clonewheel, and key-based electric guitar. I rarely play the same solo twice.
My litmus test to avoid this problem is to see if a potential band's song list has any songs in Bb. If there are none (i.e., all songs in guitar keys like A and E), then it is a "rock band" providing the keys experience described above. But if there is at least one song in Bb, even if it appears to be a rock band on the surface, I've found a much pleasurable experience along the lines of Tom's situation.