First - Who's Driving? and what sort of "Problem"?
I my opinion:
1. Even if the pilot is doing what the engineer says he wants, the pilot is responsible for allowing the aircraft to get into a hazardous situation. that is his job.
2. If a problem arises because of the tests being run (if the test is looking for this problem)- the test has sucessfully raised the problem into view.
3. If a problem arises because of the tests being run (even if the test is NOT looking for this problem)- the test has sucessfully raised the problem into view.
Obviously, company rules may differ for responsibilities when ground running for maintenance reasons.