Well, my cat died after 17 1/2 years and before I started quilting. But, my dogs are just as bad. They can't get on the table (or at least - thank heavens - don't KNOW that they really can) but anytime a quilt is in my lap being quilted or on the floor they are right on it. And, they did find my fabric stash once and pawed it around to make a bed.
I think it is an attention thing with a dog. With cats, I think it is more of showing us who is really the boss!
Cute kitties.