Well, I got curious and dug out my manual for my sewing machine and sure enough it has a "Triple Stretch Stitch" that does what others described above - 1 stitch forward, 1 stitch back, then 1 stitch forward again. So I tried it and it does indeed make a pretty sturdy looking stitch!
Earthwalker - the book I have says to layer the applique pieces with the block pieces, and then pin them together. Then you sew the 1" strip down 1/2" from the edge of the applique, so that you're sewing all layers together at once. Looks really cool when done, I'm thinking of doing a star applique on blocks using wovens.