Peeling paint on VW Jetta

I am 70 years old and purchased my first new car in 2008. After looking at many cars I decided on a German car due to quality and finish, and eventually settled on a VW Jetta 2.0-litre turbo diesel. When I took it in for its two-year service recently I pointed out that the paint peeling on front bumper was peeling. It was a bubble that burst and peeled when pressed, but I was told it was a stone chip and therefore I that to pay $110 for the repair. I stated that I would not pay for the repair, as it was a paint problem. After much arguing they took photographs and said they would speak to the VW rep when he called next. I am not convinced that a stone chip causes peeling. Should I do as the dealer states as he does not hold out much hope for a warranty claim?