Using they or their in a singular form is a very well-established form in historical and modern usage; the gender-indeterminate form in particular is known as the 'epicene they':
For instance, there are sections on there using this form by Shakespeare, Austen, Thackeray and Bernard-Shaw.
I actually wonder whether this might be an American thing, along the same lines as the Webster spelling reforms - the wikipedia page says that grammatical prescriptivism over this primarily occurs in America. Personally, I would say your quoted sentence is completely standard English.
I don't think that singular "they" never be used, just that enforcing its usage everywhere by claiming that the opposite is "hostile" (as this PR seems to lead to) will lead to awkward constructions.
http://en.wikipedia.org/wiki/Singular_they
For instance, there are sections on there using this form by Shakespeare, Austen, Thackeray and Bernard-Shaw.
I actually wonder whether this might be an American thing, along the same lines as the Webster spelling reforms - the wikipedia page says that grammatical prescriptivism over this primarily occurs in America. Personally, I would say your quoted sentence is completely standard English.