I don't drive an Airbus and have never been into SFO but in my 30+ years of flying have always stuck with the practice of cross-checking. If I'm flying an RNAV I will have an ILS tuned as well (if available). If I'm flying a visual, especially at night, I will have something set up to confirm the runway centreline (this may be a simple OBS). I will never blindly follow one line, even if this is the one painted out of the window.
To me, the most interesting element of this occurrence is the short conversation about there being obstruction on the 'runway'. I would be intrigued as to why the Airbus crew continued the approach at this point as they clearly had a doubt about the availability of their landing surface.
PS. My day job is flying calibration aircraft where our Differential GPS tells me where we are to within 20mm; company SOPS are that we shall have a secondary means of navigation to cross-check before descent below safety altitude and during all approaches.