'Native' ISO is the converse of 'expanded' - the former is achieved by analog gain, the latter by digital gain. So, a camera may have a native range of 100-12800 ISO (analog) with L, H1 and H2 expanded settings, for example.
The concept you're referring to is 'base ISO', and whether that matters depends on the camera. First off, not all sensors have 160 as a base - it's 100 for some, 200 for others. In many cameras, the analog gain is applied in full stops from the base, and the 'tweeners' are digitally pushed or pulled 1/3-stop. If that's the case, then the pushing adds a little noise and the pulling removes a little noise. In practical terms, it doesn't make much real difference. In some cameras, the 1/3-stops are analog gain, too.
Regardless, a blanket statement to shoot at 1-stop multiples of ISO 160 is not universally applicable advice...