Specifically in regards to product liability:

If an insured were rated by a carrier as a different type of business than they actually are, does that have any bearing on the coverage provided?

Specifically in one case an insured is described as being a cosmetic and beauty supply store, when they should actually be listed as the manufacturer of the cosmetics as they cause the makeup to be manufactured with their labels in both the US and China. While they don't own the formulas, it is their product.