Yes, but the original point was that the singer couldn't reach the high notes. Its very difficult to extend your natural range very much even with good technique & lots of prac & straining is just damaging to your voice. So the key change is to suit the singer. Guitarists/bassists should be able to play songs in any key, transposing is a basic formula.
I agree with you. I think I was misunderstood. The band should always play in the key the singer wants to sing the song.