Carbon dating is only one part of radiometric dating. There are other isotopes that have much longer half lives that are used in dating older things. Whilst you are correct that carbon dating is only accurate to about 60,000 years, that's not what scientists are using to date fossils. This is a common misconception. I suggest you do some reading about the dating methods they use and address those instead. Here's a quote; The best-known absolute dating technique is carbon-14 dating, which archaeologists prefer to use. However, the half-life of carbon-14 is only 5730 years, so the method cannot be used for materials older than about 70,000 years.Radiometric dating involves the use of isotope series, such as rubidium/strontium, thorium/lead, potassium/argon, argon/argon, or uranium/lead, all of which have very long half-lives, ranging from 0.7 to 48.6 billion years. Subtle differences in the relative proportions of the two isotopes can give good dates for rocks of any age. Scientists can check their accuracy by using different isotopes.