I had a boss comment on my 190,000 mile car once. I gave him a ride somewhere, and the cargo box on top was rattling. He thought it was a car. I thanked him for his concern, assured him everything was fine with the car, and kept driving it. A couple of years later, with 215,000 miles, I decided to upgrade, but not because of anything wrong with the car. I was tired of dragging the bottom on gravel roads, and with a new dog, I wanted a wagon so the dog could ride in back rather than in the back seat.
Whether the e-mail is real or fake, it's the image thing that really irks me. "It just looks bad..." Response: "Well, my bank account doesn't!" That is the real issue here - the image. If you're concerned about someone's well-being or even their financial health with regard to fraud prevention, you would handle this in a different way.