I have done several quilts with the printable fabric. You said you rinsed yours in water?
After you print the picture, peel the backing off and then iron on the back side of the FABRIC ONLY (not the paper) to heat set it. I use the hottest cotton setting. If you heat set it with the paper on, you are setting the wax into the fabric. The wax is what holds the fabric onto the paper. This could be why it's so stiff.
Then I hand wash mine in cold water, like use your kitchen sink, add a little mild dish soap to the water swish it around really good. Then rinse it in cold water to be sure no colors run. DO NOT wring it out but use your fingers to sort of push the extra water out then lay it on a towel to dry. You may want to square it up a bit while it's wet. I then iron it again from the back side.
now as far as being stiff? I don't think mine was that bad, I have noticed that once you sew it, it does leave needle holes if you have to redo something so you might want to be careful as not to make any mistakes.
I hope this helps you out a bit.