We consider one misconception of those who currently reject the general validity of radiocarbon (14C) age determinations older than, at most, 10,000 BP. There is an allegation that the presence of 14C reported by accelerator mass spectrometry (AMS) laboratories in their measurements of 14C infinite age (>100,000 years) organics used to define background levels, support their point of view. This article has been written for a general audience, primarily for those who have questions about the validity of these arguments. However, they may not be familiar with the literature relevant to providing a clear response to the claims of these individuals. We conclude that, in our view, of all of the possible explanations for the reports of the presence of 14C in these background samples, the least probable explanation has been advanced by those rejecting the validity of the 14C time scale in excess of, at most, 10,000 BP.