Good question Micheal.
The UK associations came first and are based on the Marilyns list of summits. The G ARM says "Marilyn list, as defined in the above references is the definitive list of valid Summits for England." So when the list is changed, the UK summits will eventually follow suit and change.
For the rest of the world the answer is it depends. Making lists of hills is something some people like doing. Making lists of relative hills is something fewer people like doing. So if there is a list of relative hills available for, say Elbonia, then any Elbonia association could base itself on that published list. Now you need to be sure the list was produced in a way that means it accurate and with a repeatable process. What we don't want for SOTA is someone's list of hills they like, but a list based on an objective measure. But if you have a list you use that.
For most of the world there are no lists. It gets hard then. You need to get topography data and run that through software that finds relative hills. Since SOTA started, more and better software has come available as has lots of data. You run the GB of data through the software and wait a while and you get a list of possible summits that need further checking against maps. And, you need to find the names for the summits.
The summits team spends hours doing this. Also prospective association AMs and helpers work with the summits team to identify the summits. It takes huge amounts of time. So if you have someone publishing a list of summits that you can use instead of having to do it yourself, then you grab the data with both hands (having checked with the list publisher that they don't mind.)
If you think you've seen nitpicking over rules in SOTA then that is nothing to depths the RHB mob go to. In the UK the OS data has known errors, a function of all mapping procesess. There are RHB members who have bought expensive surveying gear to measure summits near extremes of validity so they can remove OS errors, they have been responsible for all the recent Munro height changes etc.