"The only good point on there being a second form for Kyurem is by it's Pokedex entry in Black version. "
Actually there's a fair amount of things that, even ignoring possibilities of the other two's backstories, lead to him having a new form:
1. Lacks 20 base stat points. Usually the 3rd member will either have 10/20 more points if they're also the ones that keep the other two in check (Landorus, Rayquaza), or all have the same stat totals (ie: every other trio)
2. Lacks a level 100 move. Likely either of the two charge moves, but still
3. The biggest clue is the data itself. Kyurem has a little placeholder data thing for a form, just like every other form-holder in the game. Also, his signature move, Glaciate has a unique effect number despite being Icy Wind but stronger.
4. Also just look at him. His mouth is frozen over, he can't control his ice, one or both of his wings are broken, and his body is very emaciated. He really is a broken dragon, poor thing.