The Norcal Approach recording is no more reassuring. The transmission instructing AMX 668's turn onto its final runway heading is cut off so that the airline and flight number is not heard. And the repeat omits the runway designation.
ATC: "...maintain 4,000, turn left heading 3-1-0, intercept 28R localizer."
Unknown aircraft: "Blocked"
ATC: "Aeromexico 668 turn left heading 3-0-0."
Although later AMX 668 is directed to report established on the 28R localizer and the read back is correct. Then AMX 668 is cleared to 2,500, but after read back that is corrected to 4,000.
This exchange didn't help matters any:
AMX 668 " ..."are we clear for the ILS?"
ATC: "Aeromexico 668, uh, stand by....
AMX 668: "Roger."
ATC: "Aeromexico 668, four miles from DUYET, cleared to runway 28R
appr...correction, four miles from AXMUL, cleared to runway 28R
approach."
AMX 668: "okay the ILS runway 28R approach."
If the controller said DUYET rather than AXMUL because he noticed AMX 668 was lined up for 28L, he should have given a clearer instruction to get on the correct localizer. (SFO's own noise-abatement flight tracker indicates AMX 668 was lined up for 28L from when it first turned onto heading 290, at least 10 miles out.)
Finally, I note that at least two prior arrivals had trouble capturing the localizer and had to continue turns to re-intercept.
Combined with the tower recordings, it seems there were multiple clues for ATC that AMX 668 was not aligned properly for the approach and runway assigned, despite read backs to the contrary. Why these clues were missed is perhaps something that warrants investigation.