Junior selectees for next year's [undergraduate researcher] program are also invited to the banquet, along with their faculty mentors but neither the juniors nor their mentors are allowed to bring companions. That creates a very awkward situation in the case of a young professor advising a student of the opposite sex. The advisers sit with their students, and with the formal dress and the presence of so many couples, it's difficult to avoid the illusion that one is on a bizarre sort of date.
I mean, really, this is keeping someone up at night? I can understand concerns by new young faculty about whether you should have a drink with a student, whether you invite groups of students to your home, and how to handle the occasional student come-on. But whether to attend a formal event at your school and sit with your student, because it looks like a date? To whom? It looks like a professional event. No one is confused.
The writer goes on to say that she dressed in "dowdy attire" to avoid confusion, which I assume means no cleavage? She says that the situation is perhaps so dire, even now that she is "grayer and has tenure," that she might not go if she does not get to bring her spouse or partner.