GRRM said during the Season 3 premiere
interviews (ie end of March 2013) that he had roughly one-quarter of the book done. Cunningham is likely remembering it incorrectly. GRRM told Conan that he was writing quickly and it seems like GRRM has gotten through most of his side projects so there is some reason for hope, but 2014 is probably still not realistic. Summer 2015 is what I've been thinking for the past two years and it's still probably the most likely target.
Besides, GRRM's own estimates are notoriously unreliable, 3rd hand information from an actor is probably not worth much, especially when it contradicts GRRM's own words.
GRRM due to his status can have an expedited process and doesn't have to wait for the printers to open up. They rushed ADWD through in IRRC 3 months, but I hope they actually take the time to edit it this time.