Can A Business Owner Own A Business?

I read a story yesterday related to a lawsuit filed by a young woman whom was fired for refusing to remove her religion related headscarf (hijab) while on the job. My thoughts related to this make me wonder if a company truly has the right to run their company the way they would like. I sympathize with the woman but at the same time I believe there is more at stake here than ones religious beliefs. When one creates a company many things are considered and often these are related to a company image. Logos, business cards, commercials, dress codes (uniforms), jingles/slogans, and location are just a few of the things that are considered and cost big dollars by the business owner in creating a company image. These things also relate to the consumers the business might want to appeal to. If a company cannot run a business without a lawsuit related to the image that they wish to portray then is it really I privately owned company? I just don't get it because in America we do have choices and I am convinced that employment could have been found to accommodate her religious beliefs. If this lawsuit is they way it goes then maybe business owners do not truly own the controlling interest in their companies.