You are incorrect, but only technically. You can opt out of EDDM at the DMA website, but the whole chain of custody for handling the opt-out is so convoluted that it's effectively pointless.
What happens is that the DMA maintains an opt-out list which the mailers are supposed to check. Then they add your address to a cover sheet called a facing slip which they pass to the local USPS when they hand off the ads. The USPS is then supposed to give those addresses to the mail carrier and the mail carrier is supposed to check it when delivering the ads.
In reality, since EDDM is intended for blanket coverage of local ads, practically no local advertisers bother or are even aware of the opt-out list, and even if they did the mail carrier will probably ignore the list, so signing up has little effect.
The best way to "opt out" is to be a dick to your mail carrier. Put a sign on your mailbox that says "NO EDDM: unaddressed mail will be refused" and then follow through on your threat by forcing your carrier to take back all EDDM ads the next day. My mail carrier quickly realized that there was no point delivering EDDM ads to my house.