I use copy paper all the time for paper piecing. Sometimes stitches do pull out. Try to pull the seam from either end to make it taut, that helps. Also if you do wet the paper, BEWARE, a lot of copy inks run like crazy and will stain your fabric permanently! I learned this the hard way - black copy ink on ivory fabric. Also, if you can crease or fold the paper against the seam, this will help release it. This is especially easy on seams joining blocks together. Good luck! Paper piecing is not supposed to be icky!