What you ask is a valid question. Basically the answer is that ICAO does not make it clear and that every state should publish its own rules based on ICAOs.
If you look up the UK system for example it shows the minima for both aircraft travelling to, from and one in, one out from VOR/DME/TACAN (however uses 20 degrees as minimum, the use of 15 degrees is a whole other discussion!)
see Section 1, Chapter 3, page 5 of MATS Part 1 from the following link
http://www.caa.co.uk/docs/33/CAP493Part1.pdf
I do know of another ICAO based country that uses procedural seperation a lot. They do have rules regarding aircraft reporting crossing radials, and also less than 15 miles DME if the aircraft are further apart either established on, or crossing radials that are further apart than 15 degrees.
As you see you can get an answer dependant on the country the ATCO was trained in.
So if your country hasn't published its own rules then you have to stick with the ICAO grey ones. Sorry about that.