If you read the second paragraph, it claims that the resistor and capacitor are in series, but they are both connected to same positive potential and both lead to ground, so isn't this a parallel configuration?
Two dipoles are in series when the same current (same electrons!) are flowing through them.
They are in parallel if they are subjected to the same voltage (they are connected to the same two nodes at their terminals).
So yes, they are both in series and in parallel. It's not a problem --- it's like to ask if a runner in a party of two is the last one or the second one ;-).
It doesn't really make sense to consider this circuit a parallel configuration since there is no input at the node between the resistor and capacitor. It is simply a charged capacitor discharging into a resistor.
$$i_R = -i_C$$
When there is only one current path, it is a series circuit.
If you look at the diagram, you will see that one resistor terminal is connected to one capacitor terminal, and the the other to the other.
That means 100% of the current flowing in the resistor goes into the capacitor, and vice versa. This is the very definition of a series circuit.
Incidentally, one of those nodes is connected to ground. And the other is labelled +v. This doesn't change the connectivity.
If you want a meaningful parallel circuit, then you need a third current path (not just a high impedance meter) connected between the v node and ground, for instance a current source, another resistor, anything that will take a current. Then you can get different currents flowing in the R and the C, and the parallel description becomes worthwhile.