If I were to imagine what DD8 might have been like at 4, had she been tested, then it probably would have looked about like what you have described. DD was the one at the 2-3 year-old "mommy and me" classes who would wander off from the group when it no longer suited her and would go play with something else. It was rather embarrassing that I often could not entice her to come back and participate if she decided she was "done." I knew she was bright, but compliant - uh, not so much. By the time she was 8, she had taken tests at school and DECIDED SHE wanted to do well - and I am happy to report, she tests very, very well.
On one hand, I am sure the tester is familiar with different personalities - perhaps he/she can figure it out?

Otherwise, you might just have to wait a bit longer to get test results that really show his full abilities. Best of luck!