Textbook solutions are good for those that aren’t in school, aren’t in formal programs and have no other way of receiving feedback.
The “you should know if you’re right” mentality doesn’t necessarily fit a person that’s been working for 10-years and has been out of the academic mindset. One that is a beginner and could easily fool themselves into thinking they have a correct answer.
It doesn’t allow for correction of false thinking. Anyone can think their proof is correct. But fewer beginners can properly recognize when they are wrong.
This sort of mentality is a bit elitist and gate keeping.
In the end, he was like "Oh my bad," and corrected his mistake. The point of the story is that they were able to essentially ask him for the solution and they were able to check what they'd done, and in the end he made the mistake. In situations like this, he should provide the answer if nothing else to show that he didn't make a mistake in the problem set. People are fallible, no matter how brilliant you are.
In retrospect I think it was a great lesson for my future career as a data engineer. Doesn’t matter what the source is, any datum can be just plain wrong.
As in, it escaped the gravitational field?
I had a industrial engineering teacher that did something similar. Every team had a (fake money) budget for each project and bought materials from him (sole source). He'd randomly cut corners, to keep everyone on their toes. Good lesson for the real world.
Even if you do have a similar proof to the one in the answer key, that doesn't mean your proof is correct. Correctness can often hinge on very subtle distinctions. You really need a TA or instructor to read your proof if you want meaningful feedback.
One of my colleagues suggested setting up a "club" on PerusAll (https://app.perusall.com/welcome) or something similar that would allow people to discuss to book and/or work through problems collectively. (They have a club for CLRS, for example.) Right now all their "clubs" are restricted to books with Reputable Publishers (ptui), so they might need some persuasion.
Without solutions at the back of the book, self-directed learners can't verify their own work. Don't cut out the less privileged learners from bettering themselves just because you have no concept of discipline.
As long as cheats are only available for ungraded homework/self assessement tests cheaters are only going to cheat themselves.