Radiocarbon dating of animal tissues is not how the age of the earth has been established; your citation holds no sway over the dates in question. Also, it demonstrates a remarkable (likely deliberate) ignorance of what Libby's method is actually designed for, which is testing fossils, not fresh samples. Any first-year archaeology grad knows that the accuracy of radiocarbon dating goes up over time.
Simply by looking at the number of by-products of radioactive decay in ordinary rocks, we can tell that the earth must be millions of years old at a bare minimum. If it were only 10,000 years old, the atmosphere would still be toxic.