I too was under the impression that ATC were to handle any slot ammendments 30 mins prior to CTOT, which was one of the reasons that prompted me to raise the subject in the first place.
In days gone by (prior to NATS) I worked very closely with BA ops and a more proffessional bunch of people you could never meet. (Incidentally it wasn't BA that prompted me to write initially!!) However all though we are supposed to work as a 'team' it does feel sometimes when you are sitting there trying to explain to a driver why he has missed his slot that maybe we aren't all playing for the same team.
I'm all for visiting an ops room so as to broaden my knowledge and would hope they would want to visit us at some point so that we can give our side of the story!! Remember, knowledge is power!!