Is Public Shaming by the Church Legal?

From an article of the same title on abcnews.com:

A female member of the Watermark Community Church, a non-denominational evangelical church in Dallas, Texas, reached out to her pastor after her husband had an alleged affair with another woman. But when the husband, identified only as "John Doe," failed to reconcile with his wife, he said the church's minister, Todd Wagner, shamed him from the pulpit. And the minister didn't stop there. When the husband tried to resign from the church, Wagner allegedly threatened to mail a dozen letters - half to Watermark Community Church members and the other half to members of other churches who know and have worked with John Doe - detailing the alleged affair. Kelly Shackelford, chief counsel of the Liberty Legal Institute, a Texas organization that fights for religious liberties, said the church is behaving this way because it feels it must save the marriage. "They love this individual," Shackelford said. "They love the people around him and want to do everything they can to bring him back into the fold and get his life straight on path." John Doe does not feel the love. He is suing the church over the letters and said he is no longer a member. But the church says its covenants, which Doe signed, does not allow members to leave the fold. "All members submit themselves and may not resign from membership in an attempt to avoid such correction," Shackelford said... A Texas appeals court will decide whether the Watermark Community Church went too far in its attempt to save a church member's marriage. A lower court has already ruled that the church is free to release private information about its members. John Doe's attorney says his client is now considering a civil lawsuit against the church for slander.

You'd expect an article with a title like this one to include some discussion of the legal issues, but it doesn't. The public shaming is probably not an effective method discipline these days, but it'd be interesting to hear what the relevant laws are...laws against slander, I guess.