The 777 is pretty robust when it comes to Autolands, but that's besides the point really. As part of any Airlines LVP approval, we need to demonstrate competency every 6 months which usually involves a rejected Takeoff and Missed Approach to the Aircraft/Approval limit, which would be Cat IIIB in the 777.
End of the day, the instructor (or perhaps the training matrix) chose an A/P failure rather than an ILS failure (for example)...