I'm actually someone who has worked with IQ scores in my past job as a special education case manager. I *have* worked with students for whom an IQ in the 20s range has been obtained, using nonverbal cognitive measures.
Too many laypeople conflate a full scale IQ score as being the end-all, be-all of intelligence. It's not. They also imagine that IQ is all about literacy and numeracy. It's not. Far too many people equate intelligence with academic performace and verbal intelligence processing, and it is definitely not the case.
Valid and reliable IQ measures, in my opinion, only come from individually administered cognitive batteries on a one-on-one basis. They not only measure verbal intelligence but visual-spatial processing, long and short term memory processes, and processing speed.
In my experience, many academic problems stem not from a lack of verbal intelligence processing skills but from long-term memory retrieval processing, working memory processing, and processing speed. It is indeed possible to have a high verbal intelligence score that skews the full scale score high...but have an abysmally poor memory processing score that impairs performance.
And, that said, unless someone has gone through a special education assessment or intensive testing through a licensed psychologist, they've not experienced a valid and reliable full cognitive battery. The paper and pencil tests really only measure verbal and mathematical reasoning.
Oh. Those students in the 20 IQ range? Impairment in verbal measures coupled with processing issues. But definitely teachable. Definitely capable of contributing positively to society--and in many cases, more so than many of those who puff up their chests and brag about their high verbal IQ scores.