I have worked in candidate evaluations for a top finance company as well as some smaller companies and non-profits.
On listing them:
My recommendation to the OP and others is to not list or send your references on your resume unless it is specifically asked for upfront, and despite you suggesting that all employers ask for them, I disagree... Most companies, if they ask for references, will do so only after an initial interview. The benefit of this is that you can inform your references ahead of time that you are interviewing with a specific company for a specific position. As someone who has been a reference for several friends and colleagues, it's always great to have this heads up.
On calling them:
At my current firm I would say I call references around 50% of the time. We don't really have strict criteria and I would say its more at the hiring managers discretion but below are a few scenario's where its more or less likely that we call a reference.
More Likely to call: Short tenure at previous positions, applicants who apply via web (vs. referral or recruiter), applicants for managerial or high business risk positions, applicants who make claims that we want to validate.
Less Likely to call: highly technical workers who can demonstrate that aptitude in an interview, kids right out of school, referral's or candidates from trusted recruiters, people who come off as very open and honest (it's a managers bias opinion)
On whether or not its rational:
I am a big proponent of holistic hiring and grading an applicant on the full package. I want as much data and info on a person when making a hiring decision, even/especially if that data paints the candidate in a negative light. Nobody is perfect, which is why we still love to ask the question "what is your biggest weakness." At the end of the day I have a picture of my candidate that tells me his/her experience (1-10), his/her aptitude for learning (1-10), his/her culture fit (1-10), and additional measurements based on the position. Any company that doesn't strive for learning as much as possible about their employees is doing it wrong / irrationally in my opinion. People are the most important part of any company and the consequences of hiring wrong can be catastrophic.
Don't think its a great example of "people wanting to die" as others have said below and gone into detail. I'm choosing to add to the conversation because I think there is a great takeaway from this and that is people value life for different reasons. They can crudely be defined as "simple-minded" or more appropriately "traditional" and represent a very large percent of the population. Those of you who grew up in rural areas like myself are likely very familiar with the archetype described by the OP. I think a great question from this is...
Should we be encouraging people to seek out a life with more questions, more complexity, and more interests. Or should they be left as they are? This is a big political and sociological question. Should those who wish to live a more simple life be allowed to do so, and if so would that interfere with a more erudite population? (I think it may already be doing so). Should our approach be to evangelize, or should it be more of a separation / detente?
My suggestion would be for your brother to pursue education in an area that is important, yet less familiar to him. Depending on what he chooses can help dictate the where he lives and how he could fund it.
Ex. I recently took 5 months in between jobs that were largely managerial and qualitative in nature to participate in a full-time code school program. Besides the practical use of learning to code, the greatest benefit to me was in the way it pushed me to be more structured with my thinking and explicit in my instructions to others. As your brother is a CS/Math major, I would think something along the lines of philosophy and history might be interesting topics to explore. Below are some examples.
What to study: History/Philosophy
Focus: Modern Philosophy and the making of the modern world
Where to live: Paris, London, Berlin - Bonus points if you live with a local host family
What to read: Hobbes, Rousseau, Locke et al.
What to do: Learn the basics of another language, travel, experience the culture, and connect it to your readings and apply your new found appreciation for history and philosophy to your work. It will help you frame your arguments.
How to fund: English and Math tutoring
What to study: History/Philosophy
Focus: Ancient Philosophy and Alternative Economics
Where to live: China
What to read: The 5 classics, the 4 books, History of China Podcast (its excellent), Poetry, Communist/Maoist lit. etc.
What to do: travel, learn about Chinese culture and basic Mandarin (Peking Uni in Beijing offers courses in culture and language at a fairly cheap rate)
How to fund: English and Math tutoring will work most anywhere, but China has more options for Americans in terms of paid gigs. He would be a hot commodity in China.
Bonus Points: Focus on physical fitness and developing a routine to manage physical health (prep for life at a desk)