Actually, it is your problem. If your "independent contractor" is dodging taxes, gets caught, and for whatever reason is unable to make good to the IRS you can become fair game.
You can file a form 1099-MISC to protect yourself.
Even if the "independent contractor" is honest as the day is long and you know for certain sure he is absolutely legal and pays his taxes in full, your filing of the 1099 is mandatory if the payments exceed $600.
Wow, tax law sure is onerous isn't it? No wonder us conservatives moan about it!!