Suppose you found a piece of charred wood that was buried 100 feet deep. Now you want to date it at a radiocarbon lab. Could your sample be a thousand years old? Maybe ten times that!
The most advanced method to obtain radiocarbon dates is AMS (Accelerator Mass Spectrometry). If this really gives an absolute age why do I need to answer the question "what is the age of your sample?" on the submission form?
The Oxford Radiocarbon Accelerator Unit (UK) have this in the instructions for their sample submission form: "Period (required) - indication of likely age of the sample: e.g. Bronze Age, Paleolithic, Holocene etc." If 14C dating gives the exact time when the specimen died, why ask?
Check out this form from the University of Waikato (New Zealand)*:
Likewise, note a similar pattern from the Keck AMS Lab (UC Irvine):
Stuart Pocock (Clinical Trials) said that, "randomized controlled trials are an essential tool for testing the efficacy of therapeutic innovations."  Why don't we apply the same standard to radiometric dating?
Philosophy professor Alex Bird (Univ. of Bristol) explains the "double blind" procedure**:
... neither the patient not the clinician knows whether the patient is receiving the treatment. This is often done in conjunction with the use of a placebo, which is a harmless substitute equivalent in appearance to the treatment. 
What if we dated samples (even dino fossils) using the double-blind method? Mark Armitage has made a riotous LOL video on this topic (worthy of SNL). Armitage sent shockwaves through establishment academia when he found soft tissue in dino remains and later lost his job‼ In February 2013, he published his astonishing research in Acta Histochemica, a mainstream journal on cells and tissue. Two weeks later, he was fired from California State University - Northridge where he managed the biology department’s electron microscopy. He was apparently let go because of his young earth views.
*forms modified slightly, see link for the exact format, no wording was changed (e.g. "what is the age of your sample?")
** special thx to Tom Shipley for the "double blind" aspect
1) quoted in Philosophy of Science by Alexander Bird (McGill-Queen's Univ. Press, London, 1998), p. 256.
2) Bird, p. 257, emphasis added.
FYI: I heard Ray Charles live at the 1989 Olympic Festival which was held in Oklahoma City & surrounding areas. Ray Charles (d. 2004) was an avid chess player.