I've been able to confirm that the issue was with permissions! Not the permissions of my app, but the permissions of my FB page that I was intended people to Like.
My FB page had an age restriction of 18+ which was causing the issue. I removed the restriction and set it to 13+ and the jsFiddle code worked as expected.
I wouldn't have been able to come to this without the help of zeebonk who gave me a straight forward test to run which allowed me to begin the process of deduction. :)