The link is not working Nathan.
I think you may need to use different terms.
Stone foundations are just the layer of stonework which is normally at the base of a wall and is shallow.
You may need to look for 'building stone walls for basement wall construction."
I came up with this;
how-to-build-a-stone-wall in a house
The main issue you will have is soil pressure on the outside and moisture problems as well.
Both can be dealt with, with good design.
This page explains the difference in design principles of retaining walls, your basement walls with soil behind are essentially 'retaining walls'.
geotechnical/retaining-wall-types-use