I think it would be reasonable if the repair was done before the warranty letter was received, and if the independent shop's charges were in line. Otherwise, I think the claim could probably be disallowed (in the first case) and perhaps only partially reimbursed in the second.
We all have our opinions about what constitutes fair treatment, or what is "bull," but there is a tendency to lose sight of the fact that warranties are almost invariable limited, by time or mileage, and VW does appear to be taking action on issues that arise- whether it be the turbocharger, high pressure fuel pump, or exhaust flap. Now if those of us driving AdBlue cars could only get a nice warranty extension on that pesky tank heater......