There have been other posts about this recently, but English does not have a non-gender-specific singular pronoun. We only have his/her. However, of course there are times when you do not wish to specify the gender, you don't know the gender, or you are talking about a non-specific person. In this case, we use "their" regardless of its normal usage as a plural. So:
"....just because their face was plastered....." is correct.
A child doesn't have to go school just because their mum tells them to.
An employee has to start work whenever their boss tells them to.
I wouldn't buy a car from someone just because their sign said "Cheap & reliable".