No, it's not a problem of friction.
If you think the coin as a flat cylinder, the axis of the cylinder will have to rotate in order to form always the same angle with the surface of the funnell.
The coin rolls about his axis, but the axis must make a precession like movement (as if it was a spinning top).
It will behave like a gyroscope.
If the precession velocity of the gyroscope is not the same of the angular velocity of the coin around the funnell, then the coin will finally fall or follow an erratic path.
For your problem you are ok, the answer you gave is correct, I think that the gyrscope behaviour is advanced for your class.
In real world that coin would make an erratic path.