One reason to veto assert() is that it's possible to write code that works correctly when NDEBUG is defined, but fails when NDEBUG is not defined. Or vice versa.
It's a trap that good programmers shouldn't fall into very often, but sometimes the causes can be very subtle. For example, the code in the assert() might nudge memory assignments or code positions in the executable such that a segmentation fault that would happen, does not (or vice versa).
Depending on the skill level of your team, it can be a good idea to steer them away from risky areas.
