This seems fishy. (What the faa guy is claiming)
Its true that gs squared divided by 11.3 = pivotal altitude. And that due to acceleration during decent, decelerating during ascents, the pivotal altitude you computed wont ever be true. But it will be close. Sometimes as low/high as 50% of what you computed.
Maybe he was trying to get a rise out of you, and get you to "prove" to him that your way is correct.? Just like you would need to with a student. I could see an inspector doing that. Kind of dumb and an excessive use of roleplaying but in their mind they are the student, you are the teacher. So treat them like one.