Basically, what is happening (per his example) is that "Johnny" liked "Vice", and what Facebook is saying is "Johnny liked Vice", and it's pulling in a recent/popular "Vice" article to expand more on the brand. To help get more likes for the brand (which is a good thing, for pages/brands). It's NOT saying "Johnny liked this Vice story", which is what he [the guy in the video] is implying. That's why it says "Related Stories", that story is related to "Johnny" liking "Vice", because it's a "Vice" story/post.
Facebook should just make it more clear that you like "Vice" as a whole, and because Facebook wants to promote that you like "Vice" they should phrase it like it's a recent "Vice" post and NOT an article "you" specifically liked. They currently have a horizontal rule with "Related Story" to show this, but that probably isn't enough since everyone is getting confused. That's the confusion here.
It's just a confusing UI/UX element, it's not like they are saying you "Like" this weird article that you never liked.
People need to take a "chill pill" over this, because it's not as bad as it seems.