So I had an interview that was like that, but I wasn’t given enough information. I was asked to implement the “inverse square law in code” ... and I explained to the interviewer who was two years out of college (I looked up all of the interviewers on linkedin, so I had a good idea of their experience and areas of expertise) that my first step as someone who hadn’t been in an academic environment or exposed to this kind of requirement for over a decade would be to research the requirement and asked if I could consult a Wikipedia article. “No, you can’t consult outside sources.” “Ok, can you explain to me the inverse square law?” “No, you should know this.”

I didn’t know that. Also, I didn’t have enough information to ask good questions, because I was pretty sure that this was an incomplete specification and I needed to ask informed questions to reach a particular implementation.

As a result, the company’s evaluation was that I didn’t know how to code.

I did that for an interview for what is now my employer. It was via Skype with a shared code editor. The interviewer asked me to implement a data structure that I had not used (directly—I'm sure plenty of libraries I use utilize it) since college, and I said as much. I told him I was quickly looking it up on Wikipedia, skimmed the article (mumbling to myself, I'm sure), and then proceeded to implement it. My candor and ability to quickly synthesize information on the fly must have reflected well on me, because I ended up getting an offer.

This wasn't at a big name tech company, though. From the sounds of it, most of those places don't give interviewers nearly as much leeway as mine had.

Exactly ! See - https://leetcode.com/discuss/career/509258/Social-anxiety-in...

But the issue is that they're not just judging you by the approach, they are also judging you by your results.

Some people, especially those with social anxiety (not some fancy psychological term, just someone who feels uncomfortable when someone is watching over their shoulder), can only achieve results if they are not judged during the journey.