This is an interesting article talking about the use of bayes in british courts and efforts to improve how statistics are used in court cases. Probably worth keeping an eye on. It might expose more people to bayes if it becomes common and thus portrayed in TV dramas.
No statistics at all.
Or to be a bit more precise: If you have good enough data to do anything useful with frequentist methods then you may use bayesian reasoning as well. What the judge forbade is using bayes to sound scientific when you can't back up your priors.
Priors don't come into it. The expert was presenting likelihood ratios directly (though in an obscure form of words).