For the same randomized experiment, under what circumstances does Y~T+G+E control possible bias in the vanilla specification Y~T+E?

a) As mentioned in the previous question, controlling G for via Y~T+G+E is never necessary.

b) If in the particular sample, G and T are "accidentally" correlated (i.e. a low probability event occurs), e.g. somehow more boys were assigned to the tutoring program than girls in the randomized assignment.