The word "treated" in wood is normally used to refer to "Pressure Treated" referring to a preservative used to prevent rot in wood. If this is what your supplier is referring to then good because the off gassing from PT is probably not good for chickens (I am guessing here?). There is no reason to "treat" lumber other than using a latex primer first to ensure the outer paint will adhere properly. If you are using stains you do not use a primer.
I have never read about a coop built with PT lumber except when used on the floor framing. She/he is also correct about letting wood dry before painting but usually purchased lumber is kiln dried during the manufacturing process. Rough cut lumber purchased direct from a miller is not kiln dried.
I would go back to the supplier and get clarification on what they are talking about.