Yes, it is somewhat odd that this Chinese laundryman would go to the expense of such a prominent disclaimer. I have never seen any similar disclaimer, even in small print, connected with any other Chinese laundry elsewhere in North America.
A check of the directory of Chinese businesses in the US (published only once, and in about 1948) shows an “O laundry” that had 7 different locations in N. Orleans. Perhaps that fact led the owner to feel he should post the disclaimer that his store was not a trust or monopolistic business.