Why do people insist on blaming users when users use things in the "wrong" way? If you give a general feedback button to a user, they will give you back general feedback of all kinds - it's not that hard to understand, really. If you want to get feedback specific to the quality of the search results, then provide another button that says "Tell us if the results you got are not useful / just spam". Be clear about what exactly the button does, and you'll get meaningful reports from the users. Note that I said another button - you always need a general feedback button for people wanting to report something else, that's how you get general and specific feedback.

Also, google is one of the worst companies, if not the worst company, at dealing with user feedback. You can't just expect people to give you feedback but never return the favor in any way. People have the feeling that giving feedback to google is like throwing things into a black hole - like talking to a machine - if you know no one will answer you and you will never know if anyone even read your feedback, not even a little thank you note or a clue that the feedback was useful, there isn't much incentive to give feedback, now is there?