What cards allow this? I would do it in a second if that was a thing I could actually have. Not 100% foolproof but I'd bet it would stop almost all fraud.
Make a purchase, then sign off on your phone (or fingerprint reader on your laptop).
It obviously won't resolve the issue posed in the article, but it is definitely a step in the right direction and many of the major CC companies are integrating more and more. In five or six years I can easily see Chase and the like giving an option to only let the physical card be used in chip-and-pin mode and to require the use of an approved service for any contactless/online orders.
Obviously the approved services thing is a concern, but not a huge one.