Thinking about this, I realize the point is that, theoretically, one can make a full on kayak with a pre-possessed tarp, a knife, and natural materials. Granted.

Such a thing should definitely be attempted, if possible.

But in the interim, I think one could do this rather cheaply with 1/2-3/4" PVC pipe, or similarly lightweight and inexpensive materials (resin impregnated cardboard comes to mind as a possible material).

The key for the natural build is the materials. If one doesn't have access to good framing materials, it won't work.