We don´t know the details of the dating mechanisms used in this particular find as the full report has yet to be published.
However, other finds in this area have been dated using carbon dating, stratigraphy and dendrochronology. Each of those methods supports a date for this culture of 14,500 - 11,500 BP
Your point about carbon dating being wrong certainly doesn´t apply in this case as there is an excellent calibration mechanism close by in the sediment deposits of the Dead Sea.
Each year, the Dead Sea lays two sediment deposits on it´s shoreline. One is white and comes from evaporation during the summer. The other is brown and comes from winter rain run off from the hills near by. There is a continous record of these deposits going back 75,000 years in places. We can also be confident that each of these layers represents an individual season as the pollen found in them shows at what time of year they were laid.
End result - we can pull organic matter from known years in these strata and calibrate carbon dating mechanisms for the surrounding areas with great precision.
Ain´t science grand!?
Carbon dating isnt mentioned in the bible so it must not be valid.