I recently bought 3 Samsung galaxy tab 3 10.1's and I've encountered the same problem.
DLNA works but no remote display (miracast) in the display settings! That's a real shame and I feel swindled by Samsung!
edit: I have just tested the app wifi display and this app digs up the hidden remote...
GUY&GIRLS
THE SOLUTION IS NOT THE FA02 RADIO FILE.
I HAD THE SAME PROBLEM.
IT'S INTERFERENCE FROM THE WI-FI RADIO IN YOUR SMARTPHONE
THATS NORMAL DUE TO THESE NEARBY FREQUENTIES. COMMONLY KNOWN
JUST DISABLE WIFI AND VOILA!
Sorry for my poor language but dutch i my native language.
Grtz!