Simpler than that, chaps.
Totally dependent on the whim of the person designing the load system and the manner in which the error analysis is done. That is, there is no reason why two similar aircraft couldn't have a (not significantly) different LMC setup.
Re loading system design in general, there is nothing sacrosanct about how things are done .. and often personal or corporate preference dictates the layout. In particular, there is no problem with raising a system materially different to that used by the OEM in the weight control manual (by whatever name known) .. I've done just that in designing trimsheets on numerous occasions .. just a matter that my philosophies differ from the OEM guys'.
Provided that the sheet is well designed, there is no problem using LMCs .. except that the stab trim is going to be a bit more in error. Then again, if we are looking at only, say, one loading station, the trimsheet lends itself to going back up to the trimline ... correcting the loading .. and then dropping back to the envelope.
As to the interaction between loading system designer, OEM, and Regulator .. that may differ between jurisdictions.
.. and please don't deify the OEM folk .. they can make as many mistakes as anyone else in the game .. in my current role, I spend a moderate amount of time arguing with both airframe and engine OEM representatives ... I don't always win the argument .. but it's always good fun. Basically, when it comes to hard design and test data, the OEM is a very valuable source of information .. but, for routine engineering work, they are just one more source for the number crunching.