You cannot be covered under anyone else's insurance policy as an independent contractor. As an independent contractor you are a separate business entity and not considered an employee under someone else's liability insurance policy. In most cases you will need your own general liability or business owners' insurance policy to protect yourself and your practice, including any of your owned property.
Claims Example: Sue Smith is a patient who trips and falls on a piece of frayed carpet in the office and breaks her arm. Sue Smith then names all doctors in the office (three total, all independent contractors) in a liability lawsuit for negligence. If there is a claim in the office where a third party is injured and you are named in a lawsuit as an independent contractor, any other doctors general liability insurance may not come to your rescue. It is always important to carry your own liability policy to protect your business as an independent contractor, LLC, or corporation.