Earnest:
I remember reading an article about this at the time and was excited about an alternative to carbon dating the destruction of Jerusalem as that's not very reliable during that period.
Even the Watch Tower Society acknowledges the reliability of carbon dating for that period (though it incorrectly claims that it is not reliable for samples older than 3500 years). Awake!, 22 November 1981, page 15:
Since we have no way of knowing how intense cosmic rays were in past ages, we are wise to accept carbon-14 dates only for the period for which the clock has been calibrated with historical materials, back to about 3,500 years ago. Older than that, they may be increasingly inaccurate.
Carbon dating can be reliable to around 50,000 years, setting aside errors that can be introduced due to corrupted samples or by not taking into consideration the environment of the sample.