The church has no legal duty do do criminal checks.
From a criminal law standpoint, that's possibly true (if so, the law should be changed!) But failing to perform the background check could be considered negligence, even if there is no statute requiring it.
I am bothered that the appeals court used such a broad interpretation of the penitential privilege. A JC is an involuntary investigation, a judicial function (just as the name states). It is not a voluntary confession of wrongdoing. It involves third parties giving testimony; it is not a private matter known only to the penitent (accused) and confessor (board of elders). Its existence (though not the charges) can be made known to the congregation in general via a public announcement similar to "George leRoy Tirebiter is no longer one of Jehovah's Witnesses," and the congregation is familiar with that practice. Other religions claiming the penitential privilege keep even the existence of the meeting private; nobody else may even be told it ever happened.
Ironically, the point of the Conti case is that the BoE deviated from the usual practice by not making the normal announcement, and that failure contributed to Conti being harmed!