Thanks everyone. I'm in touch with Dilly now. My complaint isn't a really serious one and perhaps I've never noticed Dilly here before because I've never had a problem with the website. So well done BA.
I do agree with Shinigami that it would certainly appear safer if Dilly had a BA.com address. But I also agree with others that this might not be possible given the amount of lawyers at BA, and their power over external interfaces.
But all that aside, I still don't know why MMB tells me to go ahead and choose seats when I put in this booking reference, even though it's not possible to choose seats. Hopefully Dilly can send this to the right group of people who can fix this little item.