You didn't mention any distances and a wall is a lot bigger and flatter than your average face I guess and will reflect very differently.
Sorry, but that's totally irrelevant. Any subject of any size and any contour will have differences of 'required' exposure. As we can produce only one exposure (in camera) only one small part of any subject can have perfect exposure. Richard isn't talking about a wall, he's talking about a particular point on that wall.
Everything I have been taught from every tutor says
If the light stays in the same position, and the subject doesn't move then no matter where the camera is the exposure on the subject will be the same (it has to be).
UNLESS you are metering towards the camera when already your exposure is wrong.
Sorry, but that is not only irrelevant but is also an entirely different subject. What your tutors mean is that if, for example, the distance from subject to camera is doubled the exposure will still be the same because the same amount of light is reaching the camera - at twice the distance, the effect of the inverse square law means that only a quarter of the light will reach the camera, but the light is now concentrated into 1/4 of the space, so stays the same in terms of effective power. That's so obvious and so basic that even my cat understands it, and I haven't even got a cat
Several people, including myself, have spent a lot of time and trouble explaining why only a measurement to camera can give an accurate reading. Again, it's obvious to anyone who
1. Has ANY understanding of physics
2. Has ANY understanding of mathmatics
3. Has actually tested it for themselves. The fact that some people who should know better (usually teachers rather than real photographers) say otherwise is their problem. Don't listen to them. Don't listen to me. Try it for yourself!
The only 'grey' area here is the fact that lighting is both a technical and a creative subject, i.e. lighting is science-based but the data can then be interpreted to create different artistic effects. But the fact that someone may want to deliberately under or over expose a subject for artistic reasons does not and cannot invalidate the correct measurement method.
Richard H explained it very clearly by mentioning cosine law. That's the maths base, as I have previously explained. An extreme example would be lighting a massive stainless steel machine (UV drying oven) that I had to photograph. Producing fairly flat lighting at the angles needed created a difference of SEVEN STOPS between measuring the light correctly by metering to the camera and by metering to one of the lights. You don't get that kind of difference with most other subjects, but the error can easily be between 0.5 - 2 stops. Problem is, some people don't know correct exposure if they fall over it and some people just shoot in raw and let ACR 'correct' the exposure, which reinforces their fallacious beliefs. People of my generation, who learned by doing on large format (read very expensive) transparency film had to get the exposure right every time, so we learned the theory and we got it right. That's how we became competent and is also how we kept our jobs...
Photography in general and lighting in particular isn't all about physics, maths and constant testing. It's about many other things too, including art - but if art is ALL that someone has then any outstanding results that they achieve will be down largely to luck, and they won't be able to replicate those results because they don't know how they achieved them in the first place...
So, it's generally best to start with science and then, when the level of understanding allows us to create technically good results without any conscious thought, we can introduce art, and get the best of both worlds. Arguing about science without understand the science, and trying to contradict the established science just because some tutor or other doesn't understand the science either, doesn't lead to progress.