With the freezer paper method, you fold the paper back on your stitch line when you flip to sew and then stitch right next to the paper. I'm not sure how well that would work for teeny tiny pieces. It works very well for the rays on New York Beauty Blocks and pointy stars but those itty-bitty pictorial type paper piecing patterns are a pain in the patootie no matter which method you use.
Try a few blocks with the traditional method and you might be better able to understand the freezer paper method.