So basically, when you are in spectator mode the Fleching table will be outlined like a border as if you were in survival. You can sometimes get it to make breaking particles but not breaking animations. If that's not weirder, when you try and open it by clicking right click (still in spectator) it will bring up the crafting table menu for a split second. 

https://youtu.be/7zqL0EjkcA0