You missed the sentence starting with Hence...
A new stiffness matrix is calculated based on the current conditions (new nodal locations) . A new stiffness matrix does not give the same internal forces as the original stiffness matrix.
In a linear analysis, the internal forces are equal to the external forces. There is no need to update the stiffness matrix. If you apply a 10 N load to a 50 mm thick beam and it deflects 0.0001 mm. I can tell you that if you apply 100 N, it will deflect 0.001 mm and a 1000 N load will deflect 0.01 mm. That is an example of a model where the small displacement assumption is valid and you can use a linear analysis and scale the answer for different loads. That is what NASTRAN does. Inverts the stiffness matrix once, them computes a solution for many load cases from that one inverted stiffness matrix. That is linear analysis.
The PCG solver has a convergence criteria that give similar precision to the direct solver. Read about these two solvers in this section of the help system: