Generally, the advice is sound. When the yeast is finishing up the fermentation of available sugars, the cells start to consume the intermediates produced during the Krebs cycle and some of the consumable byproducts which were ejected from the cells. If you have hit your FG and it still reads the same 3+ days later, the cells have done this job already. The yeast cells do not wait for the sugars to be completely consumed before beginning this task and will finish moping up the intermediate products of sugar metabolism easily in those 3+ days sitting at the same gravity reading. If the gravity reading does go down, then they are not finished and you should wait another few days to cold crash.