I am also dealing with a stay that didn't post properly, except mine was at a St. Regis, not a Design Hotels. The Marriott team manually posted it after I filled out the online form but their posting didn't come with the EQNs for some reason. I emailed them back asking about it and still haven't gotten a reply.

I wonder if there is some problem with manually posting EQNs and this is a case where an uninformed rep has made up an incorrect reason to explain what might just be a technical glitch.