Problem understanding CRF/Structured learning paper on Image Segmentation

I am currently reading Are Spatial and Global Constraints Really Necessary for Segmentation?, which is a paper in CRF methods for image segmentation. They are using Joachims structural SVM to learn parameters in a complex energy model. The paper compares several different methods, including one relying only on the data term.

What I didn't under stand is: why is learning a structural SVM necessary when using only the data term. To me it seems that this would just be a linear classifier. In particular, the paper also looks at a sampling approach to find parameters, which performs better than the SSVM. Again, I am not sure why this is done at all. Can someone explain?

Btw, if you are interested in Segmentation this paper is definitely worth a read.