Bayes Theorem is core to both Bayesian and Frequentist statistics. It's unfortunate that Bayes Theorem and Bayesian statistics have the same name as people then muddle the two things (like that Guardian article does).

I don't wish to suggest that a Bayesian approach to statistics is obviously dead wrong. It's just that there is a big split within statistics between Bayesian and Frequentist and the whole thing is rather contentious. A competent statistician will produce "good science" using either method but working statisticians usually have a strong preference for one and suspicion of the other.