Well, the main idea being a SAHG is not to work and be financially supported by a BF/GF. However, there is an argument to be made that if a SAHG has a business, she actually works.

I believe the point here is whether a SAHG can support herself, or does she rely on a partner to take care of her. I, myself, work from home. Am I staying at home? Yes. But do I work 5 days a week full-time, and support myself 100%? Also yes.