What totally confuses the issue is the military interpretation of the justifiable use of avoiding action outside controlled airspace. Civil ATC will attempt to provide at least the minimum separation under RAS but because it is generally against traffic whose intentions are unknown then that is not always achieved. That is why the minimum separation is so high. 5nm / 3,000 ft allows the pilot to participate in the avoidance of a collision. The only time the majority of civil ATCOs will use the phrase avoiding action in RAS is when there is a clear indication that there is a serious risk of very little or no separation. It is after all a radar ADVISORY service.
Inside controlled airspace the situation is entirely different. It is a known traffic environment ( apart from useless class E airspace ) and the service is radar CONTROL. Within that airspace we achieve separation not attempt separation. The pilots do not have an option to decline the instructions without very good safety reasons. ATC are working almost all the time on minimum separation which is perfectly safe and helps pack the airspace as as much as we need to keep the traffic flowing. As a result when it goes wrong and ATC need to turn an aircraft for avoiding action it is possible that MINIMUM separation has already been eroded and we want you to turn urgently.
To back up this theory I put forward one requirement from the CAA. If a civil ATCO uses the words avoiding action they are required to file a CA1261 ( Mandatory Occurrence Report ) If the situation has been caused by that ATCO, even if minimum separation was achieved by the action, then they are likely to have their licence suspended and be required to retrain. Not the sort of thing that SRG are likely to be interested in if you have used the phrase to avoid a boundary of controlled airspace which contains no aeroplanes.
The phrase is overused in the military and thankfully infrequently used in civil ATC.