People have stopped believing that the Shroud of Turin is two thousand years old. Scientific tests show that it is not.

People should now require that the fragments of Australopithecus, Homo erectus and other supposedly million-year-old fossils be chemically tested. After the Piltdown Man was debunked by fluorine testing, chemical testing of the bone material has generally not been allowed or mentioned in paleoanthropology. Those who find fossils can choose what types of study should be done, and who should do the studying. The material is fragile, valuable, and reserved for study by the finders. This policy encourages scientists to look for more fossil material, which is always paltry.

Bone material slowly absorbs fluorine from the ground. The longer a bone has been buried, the more fluorine it will absorb. Read this article in the British Journal for the History of Science: The quest for an absolute chronology in human prehistory: anthropologists, chemists and the fluorine dating method in palaeoanthropology, by Matthew R. Goodrum and Cora Olson, British Journal for the History of Science 42(1): 95–114, 2009. 

Most of the fossil fragments that have been found in East Africa were lying loose on the surface, which has a known age of a few million years. These fragments are called "surface finds." It is assumed that surface finds were recently eroded out of the ground, and had not yet decayed or been washed away by rain. Nothing more is found from digging. This was the case for the Lucy fossils, and all the 33 hominin fossils that had been collected from Laetoli as of 2011, when two volumes with 1000 pages of scientific papers were published: Paleontology and Geology of Laetoli: Human Evolution in Context  Volume 1: Geology, Geochronology, Paleoecology and Paleoenvironment, Terry Harrison, editor, 2011

Paleoanthropology reports never mention fluorine testing or other chemical testing of the fossil fragments. If anyone knows of such an example, please tell me about it.