I don't believe I have it backwards or incorrect, while I believe you are also correct that happiness can be found through action and responsibility towards others as well.
Happiness and action go hand in hand. Someone who's happy is more likely to be productive, and someone who is productive is more likely to be happy.
If you want people to be more productive, help them to be happy and to learn to find happiness and contentment within themselves. If you want them to be happier encourage them to be more productive and so on. They reinforce each other, but it's up to each one of us what happiness/contentment/productivity means for our lives. People are always going to judge regardless of what you do, so just work on yourself and don't worry too much about those that judge and criticize.