it's "their" that's probly supposed to be considered singular - the egregious "singular they". the Chicago Manual of Style notes:
"On the one hand, it is unacceptable to a great many reasonable readers to use the generic masculine pronoun (he in reference to no one in particular). On the other hand, it is unacceptable to a great many readers either to resort to nontraditional gimmicks to avoid the generic masculine (by using he/she or s/he, for example) or to use they as a kind of singular pronoun. Either way, credibility is lost with some readers."

I think the fallacious word in this latter is "reasonable".

-joe (multiple choice in rants) friday