In, Granada Corp., et al. v. The Honorable First Court of Appeals, 844 S.W.2d 223, (Tex. 1992) rehearing overruled), the court stated that the producing party must do more than show that the document was produced inadvertently. "[T]he producing party has the burden of justifying preservation of privilege by showing that the circumstances demonstrate the involuntariness of the disclosure." Id. at 227. The court found that the producing party did not take advantage of all the possible opportunities to prevent involuntary disclosure. Specifically, the documents at issue weren’t segregated in the initial review of documents, the attorney who reviewed the documents prior to production did not remove the documents at issue, and the documents weren’t removed after the requesting party reviewed the documents and provided the list of documents it wanted to be copied. In addition, the production of the documents at issue wasn’t discovered until a year after they were produced, when the documents were marked as exhibits in a deposition. Therefore, the court ruled that the producing party waived any claim to privilege because the producing party failed to meet the burden of establishing that the disclosure was involuntary.
edit - that's from the State Bar.
If they're going to claim privilege then they'd also have to explain why they didn't produce documents responsive to the required disclosures -- a subset of what they disclosed. IMO Jones and Reynal are SOL.