As per the article: she was supposed to drive to places for work with her own vehicle. Old vehicles have a higher rate of having mechanical issues, making it less likely for her to be able to reliably do the job. I can see the logic that an old car impacts her ability to be a property manager in that situation.
Of course, I would argue that if the boss wants me to be places, he better provides a company car. I guess a place that is so dingy to make someone use their own ride for official business is not a place I would want to work for in the first place.