I think the distinction between "white-knight" and non lies in the horse. There is some application of white knight to what we would deem a "knight in shining armor." I would think TLG decided on the title, simply because this knight comes riding in on a sweet (white, mind you) horse with barding and armor. Not only that, but giving him an exclusive title, and putting him in a larger, more-expensive set may make sense in a marketable way.
For example, kid A and B.
Kid A: I just got this really cool knight in the gatehouse raid and/or Dragon Mountain set!
Kid B: He is cool, but not as cool as MY "white knight" with horse and armor!
Kid A: Oh man, my guy isn't the "white knight?" He's really cool, how do I get him?!
Kid B: He's only found in the King's Castle set.
Kid A: If I want the "white knight" I need to go buy that $100 set! Mom!!!!!!
I think it may make some sense to market a Knight with barding and armor on a horse and give him a distinction (or in this case, a meaningless title). ESPECIALLY if that knight is only found in a $100 set!
While the knight may be the same as me or you, it is not exactly the same and one who is interested in collecting, for example, has to go out and buy an even bigger set to get the exclusive "white-knight."