Your load here is capacitive, and not very "spiky" at all. KeithRB has in mind instead, switchmode supplies in which the current is drawn only near the peak of the AC waveform; their power factor is indeed poor but only slightly capacitive; though there are ways of correcting for this in very high power applications using a switching power converter on the input.
No, I am thinking of the circuit he has here. Assuming a DC load on the output, the only time the 1000 uF capacitor is fed current is when the AC Voltage through the rectifier exceeds the DC voltage (+ 2 diode drops!). This causes the AC line to spike the current to recharge the capacitor during the short time of the peak.