Interesting read on the different ways to dig a basement, it's always been a rather simple task for me as far as the excavation world goes.
Down south, most all basements are walk-outs or drive-ins, meaning you will have at least 1 wall of the basement exposed to daylight. If the topography of the lot will not allow that then you construct a slab on grade or crawl space. The frost line according to building code varies from 12-16" depending on the area, so there is no need for deep foundations to get below the frost line. Further south along the coast, you will be hard pressed to find a basement.
This is the way I have always completed this task. Surveyor lays out your "box", meaning giving you the outer most dimensions of the house, usually without any offsets. Using the "box" hubs, set up a few batter boards, offset 10' or so to allow for excavation (your batter boards become your offsets so take care with them). Add 3' to the box hubs and all the inside dimensions to allow for your over dig. Pull your strings and lay out the house and its offsets and corners, painting a line where the excavation will go. Easy thing about this layout is it's just an excavation and precision to the 1" is not required, you check your final product and adjust if necessary but with 3' of over dig it's rare unless you really screwed up your layout.
I haven't ever had the surveyor set cut stakes on a basement layout. Being a builder as well as an excavator you learn how to "read" a lot to set the basement grade. This usually entails taking the highest point of the lot and determining the depth of the basement, taking into account existing slope towards/away from the proposed home. You need to have at least 12" of foundation wall above final grade to thwart termites (something down south we really have to be concerned with) and water runoff.
Once you have your basement sub-grade elevation, you all know what to do - pull levers and burn diesel. Now if you have a "drive-in" basement you will also work your drive way and turn around at the same time while digging the basement. This is probably one of the reasons why track loaders are popular down south for excavating basements. You are building the whole site at this point, usually moving cut from the basement to build the turn around or back yard if it's just a walk-out. It's just not as efficient with an excavator to do this.
Once you get your basement to the desired sub-grade, fine grade the area and double check your dimensions. Next the surveyor comes back out and resets the hubs for the house in the excavation. Footing contractor comes in digs footings, you rarely see any footings formed in this part of the country. After footings are poured, the wall forms are set and poured. After stripping the forms, the sub-grade of the basement floor is cleaned up with a skid and 4-6" of #57 is spread, any plumbing and electrical conduit installed, grade beams dug, vapor barrier, reinforcement and concrete. The gravel drainage layer is set above the top of the footing. This is also a consideration in determining the desired clear ceiling height in the basement. You will have 8-10" of gravel and concrete to deduct from your poured wall height, so a 9' poured wall height will yield a 8' 2" to 8'-4" clear ceiling height, as an example.
After a 7 day cure time, backfill and rough grade the site in order to get ready for the wood butchers.