Re: Corp law
Literally, yes. If John Doe has a Nevada corporation called "XYZ Nevada, Inc." John Doe can do business in California.
However, XYZ Nevada, Inc. cannot do business here - except to a very limited degree - unless it has registered to do business in California by an appropriate filing with the California Secretary of State, payment of franchise taxes, etc.
As an example, XYZ Nevada can buy and own an apartment house in Sacramento without violating California law - but if XYZ Nevada hires a manager and advertises for tenants and collects rents, it has clearly overstepped the bounds and must register.
John Doe doesn't need to register, however, because sole proprietors working under their own name aren't subject to franchise taxes or filing with the Secretary of State. A sole proprietor may become subject to the fictitious business name laws if he uses a name other than his own, such as "40th and M Apartments."
All businesses are subject to local business-license ordinances in the city (or county) where they operate.