Well, I changed my booking and behold:
Thank you for your enquiry.
Emirates will absorb the cost of a passengers stay in Dubai if the duration is over 6 hours on several conditions. One of these is that there must be no better connection offered within a certain time of your departure date. Looking at your booking, we can see that you are not booked on the best connection, and so we regret we cannot offer any complimentary accommodation for you.
Cheers,