The auditor may have been peeling back one layer, and was simply asking how do you prove to your customer that your GR&R accurately reflects your true measurement capabilities.
The statistical tests for bias, stability, and linearity show the impact of the environment on the measurment system. When these are shown to have a neglible effect upon the measurements taken, then the GR&R results more accurately reflect the system's capabilities.
Depending on what your measuring, where you're measuring it, and the tolerances you're measuring to should drive what type of statistical testing you do for your measurement system analysis, as well as any stated customer requirements.
But, with all that said and done, Howard and Marc are right, these tests aren't specific stated requirements for PPAP. It's not against the rules to question your auditor, and ask him or her clarify or to point out the source of the nonconformance.