He's the hero, he didn't save her on the premise that he was promised poontang. At least not in a disney movie. She could have thanked him, and sent him on his way, and got back to running through suitors. And just because he saved her does not mean she is in any way required to marry him.
Keeping in mind that Jasmine was a modern western world woman who lived in Arabia, 800AD, and her father was a pussy..