VC Dimension of Origin-Centered Circle
What you are missing is a definition of origin-centered circles. The definition of the slides (your second link) is wrong, for the reasons you mention. The definition in the lecture notes (your first link) makes it clear that you can choose whether it is the inside or the outside of the circle which gets the value +1, and this shows that any two points whose distance from the origin is not the same can be shattered, and so the VC dimension is at least 2.