I buy whatever corn meal is on the shelf at my supermarket without any worries about contamination.
I firmly believe that much of the concern people express about the theoretical possibility of this or that product being contaminated is often in excess of what is required.
Celiac disease is not like an allergy to tree nuts. Nobody with celiac disease is going to die suddenly if exposed to a bit of gluten accidentally.
I *always* read the ingredients on everything I buy, and if the list of ingredients does not mention anything that I know is a concern, I proceed with the assumption that the item is GF.
I assume that foods are not contaminated unless I have reason to believe that they might be.
Think of a plant that produces corn meal, they probably crank out a few tons of it per week. Where is the vector for possible contamination? I don't see one.
There is safety in buying a major brand, because they produce more of the product, they are less likely to use a particular truck, silo, or milling machine for other grains.
Here in California I buy the bag of cornmeal that is labelled in Spanish as well as English. They probably sell more of it, and only deal with corn.
Don't worry, be happy.
Steve