Providing, though, that the right contracts are in place. Merely paying the full cost to the company is not sufficient to make it her car.
It could be argued, but I'm sure you'd lose the argument. A company has to demonstrate that the car is not available for private use at all at all - and that's very tough (eg see EIM23800). What kind of contract would give the employee full use of the car for private use 24/7/52, without denying the company any benefits?
Quite possibly. Flexible benefits is a fairly recent idea, and I suspect loads of people are getting it a bit wrong, or at least not being very tax efficient.