Sometimes I hear that you shouldn't plug (UPS brand X / any UPS) into (power strip brand X / any power strip) because of some interaction leading to poorly conditioned power, reduced battery life, massive explosions spattering the room with battery acid, and so on. Sometimes I hear that it's the power strip that you shouldn't plug into the UPS. What I haven't gotten is a clear idea of how reliable these recommendations are or how generally/specifically they apply.

Can anyone speak precisely and non-urban-legendfully on these UPS and power strip interactions, if there are in fact ones worth thinking about?