This lesson is about the Danish progressive construction and tries to be firm on the fact that it's not exactly understood literally as "sit/stand/lie/go and do", but rather that something is currently in the process of happening. Which is also what the English continuous form describes.
Nope, not true in any way.. The expression comes from a long time ago when the houses were covered with straw. The straw is very slippery when wet. The houses also used to be less taller than today and therefore dogs and cats used to climb there(depending on the weather outside it either kept them cold or hot), cats still do that, anyways, sometimes they were "surprised" by a very powerful rain and because the roof was slippery, they tended to fall down. That's where the expression comes from ;) I am still waiting for somebody to come with an explanation like this for the danish sentence...
The Danish constructions like "at gå/stå/sidde/ligge og gøre ngt" have the implication that the action is happening right at that moment. If you want to include "sitting", it's okay. But you should use the progressive tense in English to capture this in-progress feeling: "I am sitting and watching television."