The only thing the candidate did wrong was to even start the assignment. Either communicate that it is a waste of time and refuse to do it, or decide to do it and do it properly. No point in half-assing anything in life.
Indeed. That's why the HR person (or whoever it was) wasn't on a fireable ego trip. They just enforced their normal process that they use to not let people slip in through nepotism.
The process that they designed. This means they can change it and the excuse "I am simply following the pre-determined process" will not work.
Clearly, the process (of cutting technically incompetent people while letting through the technically competent ones) is not working properly; that alone is fireable incompetency ("You had only one job and you failed at it!").
Another fireable thing is that HR does not understand that they are under the CEO, they are implementing the CEO's vision, in the way he envisioned. But instead of that, HR is indeed ego-tripping.