I would be interested to hear how the FIA started with LSR.
It could clear up a lot of confusion.
From memory:
Before WW1, after one of the Gordon Bennet races, the national motor clubs of the main motoring nations formed the AIACR - The Association International des Automobile Clubs Reconnus (Recognized). They later renamed the organisation the FIA - Federation International d'Automobile.
Initially the organisation focussed on non sporting areas, e.g. touring, road maps, road books, hotel guides, motor taxation, etc.
Then disputes arose when various people in different parts of the World were claiming they had set World records. Some were recognised by one club, say the ACF, the Automobile Club de France,and some by others duch as the RAC, the (British) Royal Automobile Club. disagreements were generally about the validity of timing methods and also, but less significantly about the measurement of the distance. So as the International body so that there would be a common International basis for records, the AIACR or FIA laid down a set of rules. These rules were then enforced, or maybe administered is a better word, by the national clubs. this ensured some commonality between records set on a highway in Belgium, a frozen lake in Canada or a beach in Florida.
After complaints about wind advantage or getting some help from a hill they introduced two way runs with a time limit between runs and rules about how level a course should be.
As motor sport developed the FIA expanded its role to set rules for International competition. Capacity classes for records were introduced, they made rules or formulas for International racing, etc. In time as the workload grew the FIA set up a specialist sub committee, the Commission Sportif International or CSI to specialise in the regulation of International competition.
So we reach today's situation with LSR which was once the only form of international motor sport the FIA regulated becoming a small element of the many facets the FIA now covers.
At different times different branches of motor sport have their differences with the FIA, witness the long-running dispute with the FOCA or Formula One constructors' Association which is still simmering below the surface. But generally the main national clubs ensure that the international regulations respect what they want.
From what I have read on this board, some people fail to see the difference between a local organisation serving its members' wishes and an international organisation serving the international community.
I think I've got the main points correct, but I'm sure if I've got a detail wrong someone will correct me.