I want to know something: Exactly what would they do if we refused to pay for use of the sun? Shut it off? I'd pay to see you TRY and do that, just for the hell of it. This woman is crazy even if it IS legal. It's like selling your soul on ebay. (Or your Sol? Oh, that's terrible...) "Great! I have your soul! Now what?" You can't actually DO anything with the sun, except stand under it.
Oh wait, what happens if there's bad weather? Gonna buy off the sky so you can have clear days from now on? How much you wanna bet that that doesn't work? Maybe the price of the sun? Pretty sure the reason the law prohibited the buying and selling of planetary bodies was because it was just plain stupid. "I own Mars! You can't send probes there anymore!", and then NASA goes "Watch us." and the owner sulks.
EDIT: Extra thing! Why didn't they make her pay for the sun's net worth? Seriously, it's the SUN. It's the most valuable thing in the solar system next to a planet capable of supporting life! It makes the life happen, in part, and it holds all the planets in line with the assistance of dark matter. If you had to put a price tag on it, why isn't it much much much MUCH more than a person can afford?