The "accurate prediction" is a central part of Newcomb's problem. The issue of whether it's possible (I feel it is) and IN WHAT WAYS it is possible, are central to the validity of Newcomb's problem.

If all possible ways of the accurate prediction were to make CDT work, then Newcomb's problem wouldn't be a problem for CDT. (apart from the practical one of it being hard to apply correctly)

At present, it seems like there are possible ways that make CDT work, and possible ways that make CDT not work. If it were to someday be proved that all possible ways make CDT work, that would be a major proof. If it were to be proved (beyond all doubt) that a possible way was completely incompatible with CDT, that could also be important for AI creation.