>Um, I don't think we have enough evidence to conclude this. We'd need more headmasters/mistresses who died while on the job and under what conditions...<

Well, that's certainly true enough. Rowling may have told us that they were all portraits of dead people, but it hasn't been established that they all died in office. Or that the castle hasn't ever magically generated a portrait after the death of a retired Headmaster/mistress.