For a person with that background, simply sharing a relatively small private room with a total stranger can be overwhelming. It doesn't matter what trivial test you're giving them, if they're not able to think. The test is failing to actually determine if the person can do the technical part of the job, instead it's testing how the person performs in close quarters shared with unfamiliar people.
The whole giving homework for technical vetting is a great way to get around this class of problems.
If, in addition to what seems to be a technically competent individual, you find they don't perform well in-person, then you take that data and weigh it against where your priorities lie for the position.
There's a huge difference in knowing "technically great, performs poorly with an audience" vs. "technically poor, but we only tested them with an audience".
Furthermore, it's not uncommon for people who experience anxiety during the in-person to loosen up as they acclimate to the office environment and their peers. These people can actually be some of the best contributors, and it can be a very costly mistake to misjudge them. This personality type tends to be quite loyal and averse to changing positions, because the whole process of interviewing and acclimating to a new environment is so stressful to them.
You seem to have a chip on your shoulder in this discussion, are you having a bad day?