You are correct. It has to be implanted and be a machine or electronic device. My eye's lens replacement I got back in 2006 counts - unlike the old style lenses, it sits on struts and will focus, powered by the eye's muscle. People with artificial joint implants are cyborgs. A pacemaker or a cochlear implant makes you a cyborg. A prosthetic or Google Glasses or sewing a useless chip under your skin does not.
Most cyborgs are geezers. You will be assimilated... if you're lucky.
Warwick's no cyborg, he's a loon. Mann doesn't seem to be playing with a full deck, either.