I believe your friend is correct. In my opinion, you should aim to blip the throttle to get exactly the required RPM for the gear you are engaging. A few RPM up or down won't matter much, however 1000+RPM is way off.
If you wait for the RPM to drop, you are taking more time than necessary to complete the shift. Further, if you give it too much revs and let go of the clutch before the revs have dropped, you will upset the chassis.