Organic Arty:
This is a rule by agreement that dictates that you can only take arty units that are Organic to the force chosen.
Which I'm happy to play with or without.
It means:
You can't take Artillery that's bought from the Artillery Only section., or any extra arty that isn't attached directly to your Companies or Battalions Command.
Attaching a specialist team medium mortar section to one of your platoons is ok, because they become part of the organic force structure of your Company.
Some Companies have heavy sections.
For instance; the SS Offmap 120mm mortar support that is directly attached to some of it's Battalions OOB.
I think, that's the heaviest artillery assets Organically attached to Infantry Battalions.
So with the rule applied, you can't take Rockets or 150mm, extra 120mm mortars or anything else bought directly from the Artillery Section and not naturally attached to your purchased Companies.
Unless you agree with your opponent not to enforce the Arty Rule.