Fibrous composite materials can be significantly stronger than the source materials themselves. The binding agent forms a matrix which holds fibers together and so can be strong in localized fashion to hold fibers. This strength would usually result in the binding agent becoming brittle as a bulk material.
The overall strength comes from the combination of the two, with increased fracturing/tearing resistance due multiple independent fibers. Tears have a harder time propagating when each fiber needs to be fractured. Materials "fail" by cracks or fractures forming. In homogeneous materials the energy to continue a crack is generally much lower than continuing a tear. Sort of like static vs dynamic friction. Once started a crack will continue with a lot less effort leading to lower material strength. Fibers with a binding agent help prevent this effect.
A fantastic example of this effect is Pykrete which is just sawdust mixed into water before freezing. It becomes stronger than concrete (in tensile strength): https://en.wikipedia.org/wiki/Pykrete
I don't think saw dust is considered fibrous even if a tree is fibrous... I would think that to be considered fibrous, it would have to be longer in one dimension.
Saw dust isn't an ideal fibrous material, but it's still primarily composed of fibers [see 1]. Really they're a bundle of fibers. On a macro scale it makes less sense, but on a micro-scale the fibers are much longer than the micro-cracks that begin to form in materials under strain and which lead to the loss of strength or fracture we normally think about.
The overall strength comes from the combination of the two, with increased fracturing/tearing resistance due multiple independent fibers. Tears have a harder time propagating when each fiber needs to be fractured. Materials "fail" by cracks or fractures forming. In homogeneous materials the energy to continue a crack is generally much lower than continuing a tear. Sort of like static vs dynamic friction. Once started a crack will continue with a lot less effort leading to lower material strength. Fibers with a binding agent help prevent this effect.
A fantastic example of this effect is Pykrete which is just sawdust mixed into water before freezing. It becomes stronger than concrete (in tensile strength): https://en.wikipedia.org/wiki/Pykrete
Here's a link to a general material science intro on composites if you're curious: https://in.bgu.ac.il/engn/mater/Documents/LaboratoryBriefing...