Times have changed - for the better, that is - when it comes to hiring private aides directly.
State licensing for CNA's has become fairly thorough, and standardized, for most states. For example, in Florida CNA's are tested using the same written and hands-on-demonstration testing used by most states. State licensing also includes law enforcement checks, including FBI checks as appropriate, and the state maintains a database of licensees that includes, among other things, any disciplinary information. Licensing also includes continuing education (CE) requirements, similar to other licensed professions.
Professional liability insurance is now available for individual caregivers. It's generally affordable (to the extent that the insurance company believes the caregiver to be a good bet), with high 'million dollar' coverage.The person you engage should have a professional liability (malpractice) policy. That they've obtained, and maintained, insurance coverage for this is a good indicator in itself, as it is with any professional. If your favorite caregiver doesn't have a policy, you might ask that they obtain one. If using an agency - if the agency is is saying they are insured, but the individual they are providing has not obtained their own policy, it might be interesting to find out 'why not' (it's quite possible, perhaps likely, that the individual doesn't have the qualifications required by the insurer)
As to contractor status (versus hiring someone who would be constued to be an 'employee), just use a state-licensed professional who offers services to the general public (and not one 'employer'). To quote the IRS on this "the general rule is that an individual is an independent contractor if (the person for whom the services are performed) has the right to control or direct only the result of the work, and not what will be done and how it will be done or method of accomplishing the result."
In other words, use a licensed professional. The cost will be the same as - or often lower than - other alternatives.
More on CNA, HHA's and what you can expect in terms of quality: http://eldercarenotebook.blogspot.com/