There is no single correct stump grinding depth, which is why any company quoting one number for every stump is guessing. The question that actually sets the depth is simple: what is going in that spot afterward?
Grass needs the least. Four to six inches below grade, backfilled and tamped, gives sod or seed enough clean soil to root into and puts the remaining wood far enough down that it will not surface when the ground settles. This is the most common request and the cheapest version of the job.
Flower beds and shrubs need eight to ten inches, because you are putting living roots into that soil rather than running over it with a mower. Planting a new tree in the exact footprint of an old one needs more still, plus removing the grindings and replacing them with real topsoil — wood chips tie up nitrogen as they break down, and a young tree planted straight into a bed of them will sit and sulk for two seasons.
Anything structural goes deeper. A fence post, a slab, a patio, or a footing needs the stump and the major roots out to twelve inches or more, because wood left under a hard surface rots, loses volume, and takes the surface down with it. It will take a few years, and the crack will show up exactly where the stump was.
The surface roots matter as much as the stump itself. Grinding the visible stump and leaving a web of roots radiating out under the lawn means you have moved the mower-blade problem rather than solved it. We chase the surface roots out to where they drop below grade on their own.
Last decision: the grindings. They can be raked back into the hole and tamped as backfill, which is free and settles a little over the first year, or they can leave on our truck and come back as clean topsoil so you can plant immediately. Tell us which when we quote it.