Dating is never that precise. Carbon dating before 1400BC goes off the rails when dating known events. Any dating before then is suspect and somewhat arbitrary.
Carbon dating, properly done, is certainly more precise than to give an age of “between 20,000 and 10,000 years” for a single event. There is always imprecision in any method of radiometric dating. The article didn’t give any estimates of uncertainty for the dates, but I’d bet that they wouldn’t be several thousand years.