Counting pixel connectivity groups
N-connectedness means that from any pixel to any other within the component, there should exist a path composed of N-connected steps. In other words, as long as two groups have one connected neighbor, they should be merged into a single group. It does not mean a 2 or 3 pixel group, but rather a component which consists of linked pixels.

See the connectedness garph theory. 

With such definition, it is obvious that the author is right.