You guys all have it wrong, well BK I think gets it.
These giveaways on FB are completely for advertisement. FB is a huge diverse group of people that is perfect for a company to tap into. Once you “like” the page to enter the contest, anything the company puts up (like a new product or sale) will automatically be posted up on your feed. So now with 1 click of their mouse they can send a new advertisement to everyone who has entered their contests. Huge advertising market.
Making a giveaway or contest on their website without the use of facebook would be dumb on their part, they can reach many more potential customers with their advertisements on facebook.