Grammatical correctness is a fluid thing. "they/them/their" used singularily is one of those things that is on the edge of being accepted. Thing is, schools are slow to react and will keep saying it's wrong using a rigid form of thinking about grammatical correctness.
It may or may not have been in customary informal usage for that long [citation needed], but it is still considered incorrect in strict, rigorous, formal usage. (Yes, this is on the cusp of changing, but for now, it's still true.) In formal usage, pronouns agree in gender and in number with their antecedents.
You can easily find citations in http://en.wikipedia.org/wiki/Singular_they from Chaucer, Shakespeare, Jane Austen, George Bernard Shaw, and so on. It's not "customary informal usage", it's just a regular, ordinary feature of the English language.
