I think the poster is generally true, but I would add "in kind". The less you respond in kind to negativity, the more peaceful your life will become.
I say, "generally" because as Lynn described, negativity can come in many forms, and as Dan noted, there are some forms of negativity that require a response. Jesus' death on the cross is the ultimate example of a response to negativity!
The saying is too generic to broad application. Perhaps if it specified "negative attitudes and actions of others" it would be better. Responding kindly to a snarky restaurant server might get you better service (or it might not!).
Sometimes the correction we need comes in a negative package but that doesn't validate ignoring it. If your spouse is having a bad day, and barks at you that your outfit looks terrible, you would still be wise to check the mirror before leaving the house. Further, sometimes the sins of others toward us are the direct consequence of our sins toward them, and God's rebuke is hidden in their sarcasm and hurtful words.