Step Response RC Circuit: Current at Capacitor
Your friend is correct.  No current flows through the capacitor without some change in voltage across that capacitor.  That change - in this circuit - only happens when the switch changes state.

When the switch is closed (for a 'long time'), the capacitor is fully charged.  It has a voltage across it that doesn't change until the switch is opened.  Once the switch is opened, the capacitor charge now has to supply ir, so the voltage across the cap begins to decrease.

In the other case, when the switch is open for a long time and then closed, the capacitor initially has 0V across it and the switch closing allows the capacitor to charge.  Given enough time in this state, you will have the first condition again.