I'm not sure that every single subwoofer bypasses the crossover on the LFE input but all that I sell do. And yes the rest of your understanding of my initial explanation is correct. Just look at the manual for both sub and receiver to see which one does what.
For instance if your receiver sets a high crossover point for the FL/R speakers when they are set to small you would want to set them to large. If, however this will not allow the subwoofer to play through the LFE output in 2 channel mode (and you wanted it to) you would want to use the L/R outputs and set the subwoofer to "none" in teh receiver set-up menue. If your subwoofer uses a continuously varriable crossover rather than one with set stops on particular frequencies you may want to use the receiver for bass management (LFE output).
For instance if your receiver sets a high crossover point for the FL/R speakers when they are set to small you would want to set them to large. If, however this will not allow the subwoofer to play through the LFE output in 2 channel mode (and you wanted it to) you would want to use the L/R outputs and set the subwoofer to "none" in teh receiver set-up menue. If your subwoofer uses a continuously varriable crossover rather than one with set stops on particular frequencies you may want to use the receiver for bass management (LFE output).