The article actually confused the term (or the OP). Having had a chance to talk to some producers I now understand: "Multi-camera" productions are those that are shot live, or in front of an audience. The idea is that you only get one take, and so you shoot it from all the angles you might want so that you can cut to different cameras. In a live broadcast cuts to different cameras are in fact done live. For shows with an audience one may in practice get multiple takes on a scene, and all the cuts are selected in post-production, but it's based on the same idea of getting a "live" performance.
On the other hand, "single-camera" productions are done for the camera. They are directed knowing that all shots are going to be edited in post into a final production that will only be watched on a single screen. So every shot is blocked and lit for the primary camera, and multiple takes of every shot are the norm. (Of course, large productions will bring multiple cameras onto a set, especially for large and expensive scenes. But the concept is still a production from a single camera.)