Yani, the reason different airways have varying widths is based on the required navigation performance of the aircraft able to use that route. Unfortunately these days pilots think that because the aircraft says they are at point X they are exactly at point X when really they could actually be a mile south of point X.
For the most part these days, yes with GPS etc, aircraft are where the nav system says they are, but sometimes (even with new aircraft) they wander a bit and are up to a couple of miles of track.
So when you think you need 3 NMs left of track to get around a CB and the air route is RNP5, that doesn't mean you can help yourself and not tell ATC. The RNP5 tolerance is there to account for errors inherent in normal operations, that is, nav errors with aircraft, radar tolerance errors from our side etc. It is not to allow for intentional diversions from the published ATS route. By you choosing to intentionally go 3NMs off track you are adding an additional 3NM to the "error" for that route and that it where the problems can happen.
As someone else said, due to the congestion around Dubai these days we have no choice sometimes but to run aircraft close (not much above the minimum 5NMs). If both aircraft decide that they can wander even a mile without telling us, we have a reduction and get suspended (making the staffing situation even worse than it is, resulting in even more holding for the pilots than there already is).
Bottom line is, follow the rules and don't take shortcuts. Sorry but the end of the day it's your backside and all those people behind you that is on the line when you don't do as you should, so always ask before diverting. And to some of the pilots in the Middle East, that is BEFORE, not after having already turned 30 degrees, and then telling us that you are diverting. As I said with the number of due regard Military aircraft around who aren't talking and you may not know about, it is insane to go off your cleared clearance under any circumstance out here at the moment.
Cheers.