Yep, you're right, toilet paper, but not toilet paper alone, you have to put toilet paper all over the corpse of a living shinobi that has to die in the process, the soul of the DNA sample is summoned into the corpse with an access to unlimited amounts of chakra (does it come from the pure land?).
Rinne tensei seems a bit different than edo tensei, it seems to put Madara's life force into the dead corpse inside the toilet paper covering that already contains the soul.
Is there a Databook translation for this jutsu?
Outer path clearly absorbs something different than the souls of edo tensei, it looks like flesh, like if it was eating life force.
We saw many times that the soul can stay in the body after its death for a certain amount of time (Gaara, Naruto, Sasuke, Kakashi, Hinata...).
And everyone that has been revived by edo-tensei had still his soul in his body (Madara, Hinata, Kakashi...).
Chiyo revived Gaara using her life force combined with Naruto's.
It seems that Outer path manipulates the life force and edo tensei the souls.