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It appears that there are conflicting rules. Section 7.2 (revised edition) says: "A unit attacking must trace supply to a Div HQ to receive combat support."
Rule Section 7.6 says: "Corps units can draw Combat Supply from the Division to which they are attached, or from a Corps HQ unit."
I understand the 7.2 rule - attacks would be made at the division level (since this is the lowest commend level in the game)with division and attached assets directed by the division HQ. However, since companies are treated as corps assets, they could only attack as one of the three units attached to a division, which could put some un-anticipated restrictions on attacking when units are broken down.
I am inclined to use the 7.2 rule as a general condition and follow it as much as is practicable, but to allow corps units to attack tracing supply to corps HQ when it makes sense to do so.
I think the game is meant to be played at battalion unit level not company. Breaking down into companies is really for emergencies. I think the rules work as written and is how the designer meant for it to be played.
That being said its your game and you should play it the way you want to.