"If people think a company will pay out big dividends, then they bid up the price of the stock."

No not really and if they do then the price falls once the dividend is announced.

This is basic math:

Company is worth x dollars.

Company gives away y dollars.

Company is now worth x - y dollars.

Felix Salmon explains it well here:

http://blogs.reuters.com/felix-salmon/2012/03/19/apples-sens...