Google is under no freedom of information restrictions; it is a business. They can choose to rank mug shot sites high. They can choose to accept or not accept AdWords money for mug shot related businesses.
On the second part, sure, they could decide mugshot sites are not eligible for AdWords, but it's not great to have Google deciding who can make advertising money. OTOH, they're already doing this so I suppose they could take some sort of ethical stance here.
Another option they have is to simply set the cost of mug shot related ad clicks higher. Since their pricing determinations are somewhat mysterious, it would be harder to critique them for that. Ultimately, it would probably come down to an ethical stance for them, because they would just be making less money as a result of what I would consider to be a more ethical decision. As it is, they are making money off of a system that appears to be wrecking careers.