Since I’m evil, my theory is:
The princess arranged for herself to be the Lady, and dressed one of her handmaidens up as herself to do the hinting. Unfortunately, said handmaiden pointed the young man to the tiger. 
The king only decided which woman to put behind one of the doors. The decision of which door to open was entirely up to the prisoner. That was the sport of it, for him.
It’s a crummy story to read as a child, as most children assume the best about people and the answer seems obvious. In HS, where most of us read the story, many folks have experienced an emotional, jealous love affair and we can imagine wanting to destroy someone we’re in love with rather then let it go on without it. At this age we can at least understand why the princess would be tempted to choose the tiger.
Actually, in the original ending, the young man had spent years building up an immunity to tigers, and so was able to outsmart the kings twisted mind games.
Ah, yes, by S. Morgenstern.