I have heard this myth related to copyright but never for trademark. It would be just as ineffective as legal proof for either purpose, knowing that the post office will indeed cancel and deliver an unsealed envelope.
To obtain trademark protection, he simply attaches the brand to his goods or services and offers them to others "in commerce". Viola: trademark. In the USA those rights can be enforced in state and federal court. For somewhat simplified protection, you can optionally register the trademark in one or more states (often for under $100) or in the USPTO (starting at $265).
If he has NOT marked any goods or services (i.e., advertising for his services), then he does not, by definition own any trademark rights at all, since he has never "used the mark in trade."