I have no idea about specifics for Jeff Jones, but I can lay out a hypothetical situation as to why people would struggle to qualify.
Imagine going through most of your life without any sort of guidance or support academically. Many of the people around you, the people you love, have not gotten diplomas and don't encourage classroom effort. Kids might not be going to school regularly or put effort into learning on the days they do go. They miss a lot of basic skills required to take the exam. Yeah, teachers may be encouraging students while they are in the classroom, but to a kid, what do teachers know about life compared to friends and family? As a result, there has not been a chance to learn about a lot of background knowledge for the test. Another possible complication can arise as a lot of students from a difficult backgrounds are going through life with undiagnosed disorders making test taking difficult. Not disorders making a person "dumb" but instead things like ADHD, dyslexia, anxiety or whatever. These things could very much get in the way of doing well on an exam (especially one at that length). Add the pressure from everyone around you waiting to hear how you perform, it suddenly can become a daunting task. Congratulations on your hungover 26, but not everybody has had support and chances like many of us and it can be a difficult test for some.
Just a reminder, I do not know anything about the Jeff Jones situation. I just get annoyed when people don't consider that there are people out there from potentially tough backgrounds that make standardized tests unfair measurements of intelligence.