Ah, I think I see something you might not have taken into account.
You equated the charge coming through R1 when the diode is conducting to the charge going through R2 when the diode is not conducting. But charge is flowing through R2 even when the diode is conducting, hence not all of the charge coming through R1 is charging the capacitor since some of it is going straight out R2.
You equated the charge coming through R1 when the diode is conducting to the charge going through R2 when the diode is not conducting. But charge is flowing through R2 even when the diode is conducting, hence not all of the charge coming through R1 is charging the capacitor since some of it is going straight out R2.