Their claim was bullshit from the beginning:

Update: Cox Media Group responded by saying that it uses “third-party vendor products powered by data sets sourced from users by various social media and other applications then packaged and resold to data servicers. Advertising data based on voice and other data is collected by these platforms and devices under the terms and conditions provided by those apps and accepted by their users, and can then be sold to third-party companies and converted into anonymized information for advertisers. “CMG businesses do not listen to any conversations or have access to anything beyond a third-party aggregated, anonymized and fully encrypted data set that can be used for ad placement,” the company added. “We regret any confusion and we are committed to ensuring our marketing is clear and transparent.”

So typical advertising mechanisms, not “active listening”. Someone from marketing was too eager to sell their service.