It is a common misconception that tree roots are deep. Most of the roots are in the top couple feet of soil. This is because they need oxygen, which they can’t get if they are too deep. Only a few trees, like Oaks, have a tap root. Roots actually go further horizontally than most people think. We use the “drip line” (ends of branches draw a line straight down) as a guide. In fact, if conditions allow, roots can go 2 1/2 times as far. This is the fine feeder roots that take in the nutrients.
So it appears your neighbor is wrong in his assessment of the impact his digging will have.
I have been a certified arborist for 13 years in the Chicagoland area. You can also search the Morton Arboretum website for papers about root damage,etc