The term includes the word "sole" because it may exist only if the business is owned by one person. The IRS says "If you and your spouse jointly own and operate a business and share in the profits and losses, you are partners in a partnership, whether or not you have a formal partnership agreement."
If a business is a subsidary of another entity, that entity would have an ownership stake - That business would not then fit the definition of a "sole proprietorship". (above)