That was my reaction as well. If the other meaning was intended, I think the sentence would be better written "...marketing, storing, or packing for shipment or

That was my reaction as well. If the other meaning was intended, I think the sentence would be better written "...marketing, storing, or packing for shipment or distribution...". In that case, I think the comma after "storing" is necessary to avoid ambiguity because there are two "or" conjunctions, but at least the intended meaning is a correct interpretation. That said, I agree with other commenters that if your meaning relies so fundamentally on such a small grammatical point, you might do better using a different construction altogether.