No, it shows that that individual is capable of sticking something difficult out through the long term. Are there people without there with that quality that don't have degrees? Certainly, but you don't know whether someone without a degree possesses that quality or not (and yes, false positives are a thing, there's always a risk).
Admittedly the value of a degree has likely been diluted in recent years given that college standards seem to be getting more relaxed, but that doesn't mean that it's not still a somewhat useful signal, especially when you have to filter hundreds (if not thousands) of resumes for a single position.
Just like nobody ever got fired for buying IBM, no one got fired for hiring the candidate with a degree. Believe it or not, there may be more reasons behind this than 'self doubt' and 'insecurities'.