Pure Direct and Pure Audio modes are part of the multi-channel mode and utilize the high quality multi-channel DAC. USB Audio goes through a separate high performance stereo DAC board.
Pure Audio is a 2-channel Stereo mode where multi-channel inputs from the source are converted to 2 channel audio. Pure Direct is a pass-through (from the source device such as BluRay player) mode without any EQ effect.
Don't confuse Pure Audio or Pure Direct with USB Audio input. If you have a computer connected to HD-AVP through USB Audio, by selecting the USB Audio as input source you will be utilising the high-end stereo DAC (this USB Audio DAC has the same performance as NuPrime DAC-10) instead of the multi-channel DAC for surround sound decoding.
The L&R outputs from 7.1 outputs come from USB DAC outputs or AVP outputs. The USB L&R outputs come only from the USB DAC.  That means if you are using USB Audio as the input, there are two sets of outputs: L&R outputs from 7.1 outputs and USB L&R outputs. This allow you to setup a separate high-end stereo system in another room. Therefore, if you select USB Input as the source, then the USB DAC outputs go to 7.1 L&R RCA and XLR and USB L&R outputs.