I read this as using the profs’ threat as an example of how they could be perceived by not speaking English, not as something that actually happened. She’s a poor writer, but one that appears to be honestly trying to guide the students around potential pitfalls. This isn’t racist so much as clumsy and naive (and ironic if you consider her warning on poorly considered communication to be her downfall.) When you’re at the office you’re going to be examined in that context, and the student lounge in the dept is just like one at any other workplace. There are people who will judge them, fairly or unfairly, and as the director of the program she was just helping them keep their guard up to avoid negative consequences in the future.
However, the fact that she’s done the same sort of thing before and still can’t get the email right is probably a sign that she needs to be moved away from leadership. She’s probably a fine teacher, but leading requires different skills and clear communication is one of them.