I agree that a dollar is a dollar, but the utility assigned to that dollar is different depending on one's financial circumstances. Someone going $100k into debt (whether it be for education or a financial investment, e.g a home or stocks) may need to go through potentially years of extra frugality and/or hardship (sustenance on off brand cup noodles, living with people they dislike, or in an area they'd rather not be in, etc). They cannot afford for their investment not to pay off. It's easy for us to say (with the benefit of hindsight) that someone 10 years ago would have been better off taking out loans and investing in index funds, but as you mentioned, the past does not always predict the future, and things could easily have gone the other way (think Enron before it bellied up).
In contrast, someone with a net worth of >$1 million can easily afford to pay (and lose) the $100k and still have no meaningful change in their quality of life. To take this to the extreme, for billionaires such as Bloomberg and Bezos, they "rationally" (from their perspectives) spent >$500,000,000 on ads, and >150,000,000 on a new vacation home, respectively, and would be completely fine even if their entire investment was lost.
Edit: Just realized I may have dated myself with the Enron reference. 😛
I 1,000% agree with you, and love your step by step analysis of how you came to your decision.
I was simply responding to a post that basically said that $100K out of pocket was less expensive than borrowing. As I'm sure you know, interest is merely the price of paying current dollars back in the future, when they will be less valuable (other than computers and flat screen TVs, what costs less now than 10 years ago? -- certainly not health care, Big Macs or California real estate!), and does not make the investment more costly, unless, of course, it entails borrowing at usurious credit card interest rates in order to fund a lifestyle beyond one's means. My other post was just to prove the point using a widely followed stock index, to prove that one does not have to be an investment guru in order to earn at least as much from current funds as the interest on student loans.
Utility is something else entirely, there is no right or wrong answer, it is different for everyone, and, as you note, everyone has a different tolerance for risk. I would note, however, that the S&P 500 is a basket of 500 stocks, not one stock like Enron was. And even thought the market crashed during the financial crisis, it did come back, while, of course, a single company like Enron, or the Wall Street banks that failed, cannot. My post pointed out consistent returns over 1, 5 and 10 years.
Of course, things could change in the future, but that's not the point. The fact is, once you arrive at the decision that the extra $100K is worth the expense, it is not "more expensive" to borrow it than to write the check, due to the time value of money and the opportunity to earn a rate of return on funds not spent, even if that return is not absolutely guaranteed.
If one has available funds and is risk averse, paying cash is absolutely the way to go. But that does not mean borrowing is inherently more expensive. It's also more expensive to keep your money in a bank account than to invest in the S&P while it is going up 10% or 20%. And, of course, the availability of student loans means the opportunity to attend a more expensive, more prestigious school is not limited to those with a big pile of cash.