Don't worry about it. As long as beginners understand the camera is more sensitive to light at higher iso but the image looks more grainy it's fine.
Except that the camera is not more sensitive to light it simply produces a normal lightness of final image with less light; eg. higher ISO lightens the image.
Agreed. And the important point about the discussion is what beginners learning using that material go away thinking. And in my experience, they very often go away thinking that somehow more light gets created, somewhere, due to the extra 'sensitivity'. Mind you, I'm not sure 'sensitivity' is a concept that many beginners have much of a grasp of (nor for that matter, quite a few experienced people).
The stuff you two talk is why neither of you are good teachers.
The stuff we two talk about the concepts which need teaching is not phrased in the way we'd put it if we were teaching. And you have no idea whether or not either of us is a 'good teacher'.
You'd like to truss up beginners in fussy language and verbal qualifications which wouldn't be memorable and to the point enough for a beginner.
Not at all. That kind of fussy language and verbal qualification only comes during the back conversation, when there are a lot of people insisting that teachers should be lying to beginners. Generally, it turns out that this is because they were badly taught in the first place, and don't want to admit to it. So, what you end up with is a back discussion about what terms really mean, which them the resisters like you say is 'fussy language and verbal qualifications'.
A small example. One can choose to call how light or dark the final picture is 'lightness' or 'exposure'. The former is correct, the latter is wrong. Calling it 'lightness' sounds fussy to people who have been wrongly taught that it should be 'exposure', because they have lodged in their heads that 'exposure' is the word and haven't come across 'lightness' before. For a beginner, there is no such bias. A beginner hasn't come across either word before. They are both equally jargonised, so why not introduce a beginner to the right word? In fact, I'd think that the word 'lightness' is much more intuitively to do with how light or dark something is than is 'exposure', which as a word unexplained has nothing whatever to do with it at all.
It's very easy for a normal person to understand that if a camera is made more sensitive to light it can use a shorter shutter speed to stop action.
But it is untrue (and, as I said before, depends on a wrong definition of 'sensitivity' in any case). And if you believe it, your learning of photography will never proceed past the absolute basics (which you've got wrong anyway) because every more advanced concept is inexplicable given the misconceptions that your head is loaded with. Simple as that. Given also that you clearly don't know what 'sensitive' means, and nor would a beginner. One of the interesting things in this continuing discussion is that the miseducated for some reason think that beginners would share their miseducation. They wouldn't, unless they've been unfortunate enough to come across sites such as the one mentioned in the OP.
It is easy to visualise the exposure triangle and it works.
No, it doesn't 'work'. Even on a basic level. All the information conveys is that there are three controls. It doesn't correctly explain the relationship between those controls, it doesn't correctly explain the consequences of using each of those controls in isolation from the others. It omits the role of light altogether.
A lot of camera cognoscenti think they are superior to the 'exposure triangle' way of learning. Which is a shame, because it has worked for absolutely millions of photographers.
I very much doubt it. You're making up an estimate and you have no evidence to suggest it's correct. The triangle is recent, people who learned their photography before the millennium didn't learn it using the triangle (even if they misremember that they did). Many photographers don't bother to learn even that there are three controls (which is all the 'triangle tells them) because for them, three is too many anyway. What else are scene modes for? So, the number of photographers misled by this poorly conceived graphic is thankfully likely far fewer than 'absolutely millions'.
I think the problem lies more within the egos of those that want to show they know better, than being concerned with beginners getting bad photos.
I think the problem lies mainly in the egos of those that have been badly taught, or worse, badly self-taught and are unwilling to admit to it, so much so that they insist that beginners must be as badly taught as they were. I'm not sure why people are so eager to hang on to their misconceptions, but they are.