If that logic is extended, the true technical solution is to turn the site off entirely.

What exactly in that logic in any way leads to turning off the site entirely? It's literally the opposite: narrowing down the bots by calculating probability of them not being real people using multiple signals and like Bayesian inference or something like that, it's pretty much a primitive machine learning.

I'm surprised there are so many trolling comments here.

well if that was the case then the parent comment pointing out you could have had a false positive certainly seems relevant, but you wanted to know what their point was. I thought their point was just that these false positives could create negative consequences for anyone implementing a bot preventing solution on their site.

In the context of describing an idea to minimize false positives, pointing out a false positive in the given example is at best nitpicking, it's definitely not relevant.