ITCZ, both of your reasons given are quite correct, but they are not the only reasons. What would your altimeter read at the outer marker if you had set the QNH 10 HPA? If you were on the GS it would read 300' high but still in that small area defined by the outer marker. Would you assume you were on the wrong GS lobe and execute an overshoot or would you add the 300' to the DA? Would you check your QNH setting?
If you crossed the outer marker only 50' high, you would not be on the wrong lobe and it probably would not be an incorrect altimeter setting. Regardless of whether it is super cold or hot you must add the 50' to the DA because the error can't be explained.
The booklet you refer to does actually not say much. There are 2 references to the Markers.
4.4—FAN MARKER LIGHTS
The fan marker receiver is usually equipped with three lights—a white light which is associated with airways marker beacons and the two others (blue and amber) are associated exclusively with the ILS. These lights are mounted on the pilot's instrument panel adjacent to the cross pointer indicator. Although all fan markers are on the same carrier frequency (75 megacycles), the different lights are designed to operate independently, depending on the modulation frequency (tone) of the signal being received. A 400-cycle band-pass filter is included in the blue light circuitry and a 1300-cycle filter for the amber light.
When the aircraft is over the outer marker (400-cycle tone) the blue light flashes in synchronism with the coded signal being received (2 dashes per second),
When the aircraft is over the middle marker (1300-cycle tone) the amber light is similarly energised (alternate dashes and dots).
The fan markers serve as a definite radio fix to mark the progress of the aircraft down the approach path. The pilot normally utilises them to monitor the alignment of the glide path by comparing the altitudes at which each marker is actually crossed, on the glide path, with the crossing altitudes specified on the instrument approach chart for the facility. (See specimen approach chart at the back of this publication.)
Figure 1 illustrates the function of the cross pointer indicator and the marker lights related to the aircraft position on the ILS.
And
6 -Points to Observe When Flying the ILS
1. Carefully study the appropriate ILS approach chart before committing the aircraft to an ILS holding pattern or approach.
2. Ensure that equipment indications are normal and that flag alarms are not visible before committing the aircraft to holding or final approach.
3. Identify the ILS aurally and select the marker beacon aural switch for aural identification before commencing final approach.
4. Check the aircraft altitude through the marker beacons with the altitudes given on the ILS approach chart. This will provide a check of the glide path alignment.
The AIP states that false courses may exist or course reversal may occur outside the sector 35 degrees either side of the localizer course. (nothing said about the glide slope and in any case 35 degrees would be a loooong way off and should be apparent if the pilot has some situational awareness).
Appendix 1 of CAO 40.2.1 states the requirements for a FLIGHT TEST. The AIP states the requirements if you fly a 'none flight test ILS'. (there is also a difference for when you can commence descent on a NDB approach).
I realise that we do not fly above 100 000' but in ISA when the altimeter indicates you are at 30', you are actually only at 16' (remember we do not use an altimeter to measure an obstacle's height). The 500' separation between VFR and IFR still works because both aircraft use the same 'rubber band' and we are still well apart. At the DA we are around 1/2 that height above the ground but the ground or an obstacle does not use a 'rubber band' to measure its height.
As for your example "what would you do"?
The TAF at the 'nearby' military field would probably read pretty much the same as the destination and REQUIRE fuel to fly to a SUITABLE alternate. Therefore the problem should not arise in the first place. If I were on long haul and got my TAF 14 hours ago, I would get an update BEFORE I pass the last point of safe diversion.