I've read that one should pick an ion peak that is unique to an analyte for quantification purposes and then pick at least 2 qualifier peaks and use their ratios to identify the analyte (or avoid misidentification thereof). How exactly does this work?
This is a general "identification" rule which should not be restricted to mass spectrometry.
In chromatography you may be analyzing very closely related analytes whose masses are very close or even identical. Think of structural isomers (low resolution MS is blind to enantiomers, isotopomers, isotopologues etc.). Structural isomers may very closely related mass spectra and their molecular ion peaks would be identical in mass, but their fragmentation patterns might be slightly different. So the "good" advice is pick not one but more than one line in order to positively identify a target analyte.
Think of the legal consequences of false positives. A sportsman or women may loose their career if the tests show a false positive or a criminal may go scot free. Therefore analytical chemists have a huge responsibility on the society in terms of having a very high degree of confidence in identifying or quantifying anything.
Although most of the people think that mass spectrometer is a "perfect" detector in chromatography, it is nowhere close to being one. Many compounds do not ionize well and hence go undetected. It is extremely useful though.