Yup, that would be true if you plan to fly an Emirati registered aircraft.
You should contact the GCAA at the following:
http://www.gcaa.ae/en/?T=1&ID=30
LICENSING & AEROMEDICAL SECTION
PO BOX 30500
DUBAI
UNITED ARAB EMIRATES
TEL.NO - + 971 4 2111562
FAX NO - + 971 4 2826233
EMAIL -
[email protected]
Depends on if you want only a temporary validation of your FAA Certificate (you would need to keep the FAA one valid) or do a full conversion, which may involve an Air Law Examination. Better to write them, get it from the horse's mouth.