Root degrees need not be unique for a fibonacci heap, but when it comes to extracting minimum there exists a step called 'cosolidate nodes' where the order is checked and should not be unique. So to conclude, the uniqueness of height of the tree is considered only while consolidation steps are to be performed.
Why heighest degre + 1? what will happen if we have all 1 degree nodes and we have to consolidate 4 or more 1 degree nodes? It will need 3 degrees.... but according to the video we will only have o to 2 array indices..