The best thing for you is to either live with yours or trade it for the 2016. They will not fit.Will the 2016 Elantra head light assembly fit and correctly wire up to a 2013 Elantra? I love the look of the newer lights and I can get a set locally for cheap.
They are most likely referring to the sedan lights. Nobody would know the difference between the 2013 and 2016 since like you said they are the exact same.They fit the 2014 to 2016 not the 13
UNLESS it's the GT but they are the same so why would he want to change if it's the same.