She's right about potential danger... if the threads came off&& were ingested or got all tangled&& wrapped up on someone's tiny little foot, neck, etc. that would be no good. If you want a rope in your cage there are ways that you can braid fleece into a nice, long swing-rope.
Also, since fleece is among one of the best materials out there for suggies, you might want to make a fleece pouch for them to sleep in... I can't tell what the one you have now is made out of... cotton?