The point is, if you're going to "test" the piece of whatever to see if it's part of a "rope," you would have to have known rope fibers to test it against. There is no independent test to see if a fiber if from a rope.
So, if you had a knife known to be involved in the crime, you could test the knife for rope fibers, then test this fiber to see if it is the same. Or if you had a rope found in a dumpster with Jodi's clothes, you could test the KNOWN rope fibers against the mysterious crime scene fiber to see if there is a match.
But without known fibers, there is nothing to "match" to the unknown fiber. So nothing to test. Unless you just test to see if it matches the pillow. Which would be fine, but it wouldn't prove Jodi was lying about the rope--it would just prove that the pillows shed.