Delivery in an online world doesn't have to involve a shipment, since lots of "stuff" is delivered electronically. Sites of the type you mention may include language on their webpages that provide for a low- or no-cost initial membership or purchase, with future charges for membership renewal or additional services at a greater cost unless the consumer cancels the initial membership by a deadline. The automatic nature of the future charges is often not "clear and conspicuous."
Some of these scams are described as "negative options" by the Federal Trade Commission in a 2016 blog article at https://www.ftc.gov/news-events/blogs/business-blog/2016/09/negative-opt...
If the consumer authorized the initial transaction (you may be able to view the ad on the problem website) and the subsequent charges to the debit card, as evidenced by the merchant's providing the consumer's name and other information, the transactions were authorized, and the bank can deny the consumer's Regulation E claim.