The much more easy thing is that they reimburse you only for what you charge to the company card. This is much more feasible now than it was even 10 years ago.
I have had to occasionally expense something on a personal card and I had to get multiple levels of manager approval afterwards (not difficult, just explained the circumstance to them.)
That's something else, isn't it? Or how do you pay with those at a typical POS terminal at a random lunch place?
Any ideas why the companies in the article doesn't just do that to fight the fraud then?
But, to the degree that fraud becomes a real issue, it may be the simplest thing to do.