The entrance pupil taken as the image by the objective of the small obstruction. In this case it will be a virtual image 67.5 m behind the telescope, and not useful for determining the actual working aperture. Why indeed should it?
Ugh... Unfortunately that is optics 101 and gets to the crux of all this. That image way back there doesn't just represent the entrance pupil - it IS the entrance pupil - and it lives in object space. That hole way back there is what is seen by photons emitted by the object - and they travel all they way back there in object space - and if they go in, they go in. Otherwise they don't.
The shadow method is based on measuring the size of that thing, which is far away, based on a shadow cast by it. That is extremely problematic to do accurately when the pupil is far away.
The shadow is created by projection optics that have nothing to do with the entrance pupil in the first place - even if they use optics critical to the system itself. Any optics behind the limiting stop plays no role in the size of the entrance pupil or its appearance from object space.
There are numerous other sources of systematic error that I have not mentioned. But the simplest form of error in this measurement is that the method of "collimation" is based on setting the focus so the beam appears to have the same size at two different locations. For a distant pupil, the separation of these measurement points will need to be very great - and any fuzziness of the edge due to diffraction and aberration within the projecting optics will make it hard to match those sizes without introducing taper in the beam. Even if this is achieved, an error of 1' will create an error of 20mm for my mak. If the offending aperture is any closer to focus, the error will begin to explode because the pupil distance increases dramatically.
If the beam is tapered at all, and if it happens to be even slightly divergent, then you will get a clear shadow of the front of the objective - and you won't even see the true pupil diameter because its shadow is slamming into the back of the objective. You will get a false impression the objective is the problem - when it isn't. If the true aperture is only slightly smaller than the objective, which is often the case, then whether or not the shadow is seen depends critically on how the beam happens to have been prepared.
This means that the measurement is completely ambiguous and sensitive to the beam preparation. And this is a case that is common for people trying to measure the aperture: The aperture is potentially slightly undersized, and the obstruction is near focus.