The 4 digit passwords are used for temporary sessions for giving a remote party temporary access to the machine.
In the position of the person giving support and thus needing access, I'm already very happy when I finally get my mother to launch the Teamviewer application (finding an icon on the desktop can be so hard). I don't need her to spell out a real password for me and if she was to chose one of her own it would not be much safer than what Teamviewer generates by default.
Support sessions like that last a maximum of 30 minutes, after which she closes the application (as encouraged by the UI). I really think that the short-lived nature of connections with a weak password somewhat mitigates some of the complaints in the article.
I've also used it to help my Dad. He does the same thing, launches the application to initiate a session and then closes it when he's does. Since it's only open while he's expecting a connection, I don't see how it could be much of a security issue.
It is interesting to note, however, that a company who's product is designed to allow people full access to another computer and promotes security wouldn't have periodic security audits of their protocol to ensure it's sufficiently robust.