From The Dis....
"Annual Passholders can now add the Disney Dining Plan to their reservation. This will make the booking a package subject to the terms and conditions of those reservations. (Paid in full 45 days in advance, etc.)"
This can be found about 3/4 of the way down the page here:
http://www.wdwinfo.com/discounts/discounts-ap.htm#DISNEYDINING
I just called Disney and was told that annual passholders can add the dining package to their resort stay, but as listed above, this then makes their stay a "package" and those conditions apply.
If they were told no....I would tell them to call back and speak with a different CM.
Kevin