Many a fruitless hour has been spent in Editorial meetings and by reporters in the newsroom over the singular use of their rather than having to write he/she.
It was complicated by the fact that the slash was a command to the computer on the ATEX system we used in the 1970s.
So basically we threw up our hands and used their as a singular when the sentence could not be constructed to avoid it.
In Bingley's super link, the sentence about theft could be easily reconstructed to avoid using "their" by eliminating the "taken upon" phrase.