It is a possibly a mess in terminology done by the Author. Precisely he seems to mess the input current of the network, say$$I_\textsf{IN} =\frac{V_\textsf{IN}}{R_\textsf{IN}},$$with the true load current, i.e.$$I_\textsf{load} =\frac{V_\textsf{load}}{R_\textsf{load}}.$$In the first configuration, the load resistor is series connected to the a-to-b section of the potentiometer, thus invariably \$I_\textsf{IN}=I_\textsf{load}\$.
In the second configuration the potentiometer and the resistor are not connected in series thus it is always \$I_\textsf{IN}\neq I_\textsf{load}\$.
However \$I_\textsf{load}\$ is always proportional to \$V_\textsf{load}\$.