The undergrad courses with the highest average IQs for students are maths and physics. They are probably amongst the most difficult courses. But the entry requirements for those courses are lower than things like Law and Medicine.
Not true at all. My dd has just gone through A-levels wanting to do maths at uni. There are a number of A A A places for maths.
Oxford typically asks for A A A for maths, but A* AA for medicine and AAA for law as one example.
The difference perhaps is that you can do maths at a wider variety of places, so you can get into some places to do maths with lower grades. However it isn't always straight maths-"mathematical science" or similar.
The other thing about the statement "the grades don't mean anything" is often trotted out to someone who is disappointed. It's no comfort and in a lot of ways quite insulting to say that. You wouldn't ever say that to someone who's delighted.
In the good results level you can also have someone who is disappointed with what is apparently fine results. You can see it in the current thread about the person who has 6s expecting 8s. Most people seem to be saying "what's wrong, 6s are great". For someone who was expecting 6s, yes, that's true, but no one who was expecting 8s is going to be at all mollified by being told it's great results, and it's quite patronising to think so.
Dm was a teacher. She taught various people at various levels all the way up to degree. She reckoned the best result that she was most delighted about as an G. The girl's brother went off to do the same subject at Cambridge. He would have been disappointed majorly with a B.
There was an interesting article on the BB which said head teachers have warned that some lower-attaining pupils have been so disillusioned they refused to sit the exams or even their mocks.
Interestingly dm came across this when GCSEs first started too. She never actually had a pupil refuse to sit in the end, but the lower grades did get very negative sitting papers that they couldn't do most of it, and would get a low grade. Sometimes it took a lot of individual building up and setting realistic targets for individual children.