The Singular "They"

I just posted something like the following at VC as a comment on a post on grammar.

Prof. Volokh, I’d value your opinion on what is a much harder question than whether “Everyone thought they were right” is valid, which is the singular “they” as applied to organizations. Here’s an excerpt from a student paper: “The US Navy took the lead in this research. They saw an opportunity...” This is common in educated speech, but it is against the rules of style. It is contrary to parallelism, but in accord with the good realization that organizations are not real persons. What should we do?