My two DDs went to a GDST junior school, and one is still there in the senior school. The one who has stayed is dyslexic, as the school has a very good track record of assisting girls with dyslexia to achieve their full potential.
The junior school is hugely oversubscribed with around 10 applicants for each casual place arising. Therefore, if parents decided to leave the school because the teacher gave them "bad news" about their child, the school would have no difficulty in allocating the place. So, there would be no benefit to the school of withholding the truth from parents.
I don't know if there are any autistic girls at the school. I suspect there may well be, but it's not my business, frankly. I know there are/have been girls there who are visually impaired, and with physical disabilities, as well as lots with SEN such as dyslexia and dyspraxia. It is academically selective, so a child with HFA but who is gifted and talented may well fly through the selection process.
I really hate this kind of article, based on one person's experience of one school, that says "all private schools are like this" or indeed, if it said "all state schools....". I have experience of three private schools. Two have been very good regarding SEN. The other couldn't wait to get rid of one child with SEN, and later, when my DS was diagnosed with dyspraxia, the so called SENCO didn't even bother to meet with me to discuss it or arrange an IEP. (His excellent class teacher did, though.)
So, I could write an article that said "two thirds of private schools are very good for SEN" which would be just as accurate as the one linked to. Ie, not very.