That statement is a flat out lie.
The vast majority of scientists today conclude that carbon-14 dating is very reliable at least to 20,000 years, and many take the date to 50,000 years or a little more.
Practically all evolutionists conclude likewise.
Do you understand that not all Christians who dispute this YEC 6,000-year-old world nonsense are evolutionists?
Here is an article linked to below from a Christian scientist who is not an evolutionist entitled "How Trustworthy is Carbon Dating" you many find of interest.
You will note the author mentions some problems with carbon-14 dating but concludes:
"Carbon-14 dating remains one of the best tools for determining the age of things that lived from 500 to 50,000 years ago."
Reasons To Believe : How Trustworthy is Carbon Dating?