This all forms part of the brief and downgrade options. Ultimately you are flying using the needles but you may be using the green/magenta string to fly it in FINAL APP/ LNAV/VNAV. Our ops manual on the Airbus for example says we need GPS PRIMARY for FINAL APP and NAV-FPA. If we lose that (even if predicted nav accuracy is still high), we have to revert to TRK FPA (i.e. basic needle flying).
You need to pre-brief what you're going to do in the unlikely event your nav capability downgrades. What if the navaid is badly calibrated? What if it's a CAVOK day? What sort of terrain is nearby? Some is prescribed, some is airmanship.
Champ