As we explain in the documentation (see "Natural" in the Help Index), the NATURAL boundary condition defines the value of the outward normal component of the boundary flux term implied by the Divergence Theorem (or equivalent integration by parts). As such, the sign of the Natural BC carries the sign of the flux term in the PDE. Our examples include terms like Div(K*grad(temp)), whereas Backstrom's examples use terms like Div(flux) or Div(-k*grad(temp)). That is, the sign of the flux terms differ between the two documents. The sign of the Natural must therefore also differ between the various problems. I think you will see that this fact both explains the apparent discrepancy between the statements in the various examples, and also highlights the fact that the meaning of the Natural Boundary Condition depends on the statement of the PDE.