Can you clarify your 1st paragraph, I think you may have left out a word or two, such as "not" or a preposition or something. Thanks.
My point was that you can be an independent contractor ("IC") for one entity and not another. For example, ABC company hires you as an independent contractor to be on "loan" to ABC company's clients. In that circumstance, you may be an employee of ABC company, but an IC of ABC's client.