Things I know: RN author stated "the immediate execution" and "will be beheaded" in writing.
Why I know it: They published a photocopy of the ransom note.
Things I don't know: PR's fibers were entiwined in the garrote, how they became intwined if they even exist, why it would be significant (she's JBR's mother, naturally her fibers would be all over the place)
Why I don't know: There's no affidavit published that quantifies the fiber, the amount or type that was found. No way of knowing if it was 3 fibers or 30000 fibers. What color were they, from what article of clothing? Who says they're fibers from her clothes? Fibers aren't unique like a fingerprint, they can not be matched like DNA can. They can be fibers from ANY clothing with SIMILAR fabric. The fiber, like the DNA, is arguable.
As arguables go, unknown male DNA mixed with blood in JBR's underwear is exponentially more significant than fibers entwined in the garrote. JBR's hair would've naturally been contaminated with her mother's fibers.
Finding PR fibers on her own daughter just isn't very remarkable. In the paint tote, or whatever, its about as remarkable as finding sand on the beach.