How much can an employer hold an independent contractor accountable?

She is completely incorrect. An independent contractor's work is governed by contract, or the agreement between the person or company employing her services and her; that agreement could certainly incorporate a Policies and Procedures Manual. Furthermore, unless you have already signed a written contract with her guarantying her work (e.g. committing to using her for, say, a year), you would be well within your rights to simply stop employing her if she will not work the way you want, or  not agree to terms and conditions (or, if you will, policies and procedures) that you wish her to agree to. So if she won't work the way you insist, stop using her.

However, you may be making yourself vulnerable to a claim for FICA withholding, overtime, benefits (if you offer any to employees), etc. by the way you are doing  things. To oversimply, you *can't* hold independent contractors to a set of policies and procedures the same you would hold employees. Independent contractors are *independent* to at  least some degree--they generally determine their own way of doing things, have some say in their hours, advertise for their own customers, provide their own tools, etc. If you are telling "independent contractors" how to do their jobs, then they may not be independent contractors--they may actually be employees. The labor department and tax authorities do not care what you call a worker, what agreements they sign, or how you pay them--if the reality of how they work and how you manage them is that they are employees, then you will be held accountable to provide them overtime, benefits, make unemployment contributions, etc.

Therefore, while you can require your "independent contractors" to adhere to a policies and procedures manual, it may be that in doing so, you are actually converting them to employees. You should consult with an employment law attorney who can review the manual, how the workers actually work with you and how you supervise/manage them, etc., to deteremine whether you actually mischaracterizing  them and making yourself legally and financially vulnerable.

What the independent contractor has stated is correct. To force the independent contractor to agree to the terms and conditions of what you have stated essentially makes the independent contractor an employee of yours.

What should have been done or needs to be done is to have a business attorney draft up an independent contractor's agreement for all independent contractors to date and sign as a condition of receiving continued service and a 1099 from your business.