Is the author wrong about this RC low pass filter circuit?
The actual text quoted is not shown, but there is enough to make an educated guess. 

I suspect the intention is to consider R_L &lt;&lt; R so that the only current through the diode affects the voltage across R_L. 

The three stacked voltage sources in the second half approximate a half-wave rectified sine wave. Specifically, they represent the first three (non-zero) terms in a Fourier series representation of a half-wave rectified sine wave. 

If you assume an initial voltage for the capacitor you can then analyze the current waveform from the point where the diode starts to conduct.