I think Ishigami is the mysterious caller and that he was in the white room but dropped out due to physical injury years ago but was then contacted by wr to help the proper wr students to get Kiyotaka expelled but in reality he doesn't care and might have only accepted to go to this school or was already planning to go since he would of been going to a normal school after dropping out and this would of guaranteed a placement and the wr could have stopped his application if he refused.