I wonder if false advertising can create a legal expection of privacy. What if I sell a red filter for you to hang in your windows, and advertise that it protects against anyone seeing through. But you can just apply an anti red filter to a camera and see perfectly. Is the government allowed to do that? (I don't particularly understand optics, and this likely doesn't actually make sense, but you hopefully get the idea).
An argument can be made that if someone's using something they don't understand, they shouldn't have a reasonable expectation that it's as described, especially if they aren't paying.
Many people have misconceptions about VPNs as well. That doesn't mean the data they willingly hand over is reasonably expected to be private.
(If there's precedent for a false advertising interacting with the third party doctrine, I'd be interested in seeing it.)