The question about if you can successfully make a data quality program without doing data governance is a recurring subject in the data management realm. This question was again discussed by Rachel Haines in a recent article called Is the Data Governance Value Message Getting Lost?
I think we have used the term data quality much longer than we have used the term data governance. Before data governance became a popular term organizations did make data quality programs without doing something called data governance. However, doing something about data quality is an act of data governance just maybe without some of the formalized things we just recently have put under the umbrella called data governance.
As I remember, we have always worked with assigning responsibilities, understanding and documenting business rules and some of the other good stuff now seen to be embraced by data governance. Doing data quality improvement without such considerations has always been pointless.
Today we have good frameworks available for data governance. Of course you should take advantage of using the maturing data governance discipline to support achieving and sustaining better data quality in order to provide better business outcomes.