The selected point appears when I activate AF (I use rear-button AF). However, I cannot move it until I first hit the AF mode selection button...then that frees the AF point to be moved somewhere else with the joystick. In other modes, I just have to activate AF, then I can move the selected point with the joystick without the intermediate requirement of pressing AF mode first.
I use back-button AF, I just tap the AF-ON button then I can move the joystick to move the AF point (even after I've released the AF-ON button, although as I stated above, moving the AF point 'times out' just like the metering). That's in all modes, including AI Servo + 61-pt auto.
I dunno what's up. I'm kind of ticked, as since I reset, I now have to press that AF mode button to get the AF point movable in every AF mode. I can no longer simply tap the joystick (after initially activating AF, however that's done) to get it moving. I think something is up with my 5D III.
My 5D3 did the same exact thing right after I got it back from CPS. I thought it might be a setting, but it turned out the lock button was on. Hope it's that simple for you, I never use mine so it took me a while to look at it - that was big "duh" moment.