mainstream accepted date for the age of these bones (several dozens of million years old).
The age that these groups claim to find is usually on the order of thousands or tens of thousands of years old.
Robert Kalin senior research specialist at the University of Arizona’s radiocarbon dating laboratory, performed a standard independent analysis of the specimens submitted by Hugh Miller and concluded that the samples identified as “bones” did not contain any collagen. These results corroborated established paleontological theories that assert that these fossiles presumably were 'washed away' over long periods of time by ground water, replacing the original bones with other substances such as the minerals naturally present in the water, implying that this sample could ).
At this point, it is quite clear that there is little reason to trust the research by Miller's research group.
Furthermore, it appears less than certain that the carbon found in the bones actually had anything to do with them being dinosaur bones.
In the article by Leppert, we find: Hugh Miller generously provided me with a copy of the elemental analysis of one of their dinosaur fossils.
In this answer, I will try to go through this story in great detail, (hopefully) exposing the reasons why this work is not taken seriously by scientists.
A research team from the CRSEF, or Creation Research, Science Education Foundation, led by Hugh Miller, has claimed to have dated dinosaur bones using radiocarbon methods, determining them to be no older than several dozens of thousands of years old.The particular example you bring up is one of the most famous such cases.The claims are really quite spectacular, when taken at face value, and therefore should be examined thoroughly.And the result of this accepted method dates dinosaur fossils to around 68 million years old. Its half-life ($t_$) is only 5,730 years—that is, every 5,730 years, half of it decays away.The theoretical limit for C-14 dating is 100,000 years using AMS, but for practical purposes it is 45,000 to 55,000 years.The fluctuation of the amount of C-14 in the atmosphere over time adds a small uncertainty, but contamination by "modern carbon" such as decayed organic matter from soils poses a greater possibility for error. Thomas Seiler, a physicist from Germany, gave the presentation in Singapore.