If I am working as an Independent Contractor if the company does not send you a 1099 form you do not have to report that income to the IRS?

I wouldn't take that conclusion. It's your responsibility to report income to the IRS on your 1040's. Its the payer's responsibility to issue a 1099-MISC if you earned more than $600 as an independent contractor in a calendar year. Its possible the payer doesn't have your correct address or the 1099 was misplaced or some other reason (I have heard them all).

Take the high road and call the payer and ask about the 1099-MISC. You cant just take the position of "well I didn't receive the form, so I'm not reporting it". You have responsibilities as well.