schach

Question

I've heard that if the schach mats are held together by something that is possul for schach, then it would be possul for the following reason: The gemara talks about a case where the schach is higher than 20 amos and "hootzin yordin" (pieces are hanging down, for those viewing this) under 20. The gemara (if I'm not mistaken, I haven't looked it up) says that since if you took away the schach which is over 20, the stuff on the bottom would fall down - therefore it's possul. Is this a good parallel to the case of the mat? If you took away the schach possul (i.e., a string) the individual pieces would fall away. Make sense?