Sorry for asking! But I'm short on intelligence so can you point me to the particular words on this page which enumerate the status benefits that SkiAdcock described when booking through sites like Hotels.com?

What SkiAdcock said is perfectly true, in fact I just checked it with the FD manager of Marriott WAW while sitting in the exec lounge, but I don't see anything on the link you gave that confirms the status benefits of OTA bookings.