[yuubi]

Because of that feedback, you get to use your load as the lower half of the divider, so the total current drawn from the source is the load current plus a few microamps for the regulator's internals.

In the passive voltage divider circuit, if the load varies its current draw, you have to have a resistor in parallel with the load so that the total current through both the load and the resistor doesn't vary significantly (where "significant" is derived from your tolerance for voltage variation).