Gluten Free oregano!

I made a delicious Pozole yesterday, and was amused to see that my oregano was labeled "Gluten Free" - I was unaware that the drying and cutting process might have involved wheat.

Gluten Free Milk

Be sure to check your milk for gluten /s

I got a kick out of the product name "Dairy Pure", which would indicate that "Only Milk" is in the bottle. So, is the implication is that other milk jugs have wheat?