One reason why crosschecks are so important with an ILS is that most people think that two narrowly focussed beams intersect to provide the guidance, but they don't!
The "beams" are created electronically by the equipment in the aircraft (that is, voltages are produced from the radio signals, which drive the instruments). This means you can get on-course or on-glidepath indications regardless of your position, as was found by an Air New Zealand 767 in July 2000, which got down to 400', 6 miles short of the runway - maybe that very aircraft?
Phil