Response 1) The mass of people who claimed they witnessed supernatural events are wrong for one reason or another.
But this response destroys the Kuzari principle, because then a mass of people can be wrong about witnessed event(s). So the Kuzari proponent seems forced to select Response 2.
Response 2) The Miracle of the Sun involved supernatural events.
First - that response would lend to support to the Pope/Vatican claim the Miracle of the Sun supports the truth of Christianity. I have difficulty accepting such a notion after being taught that Christianity is a false religion.
But there are deeper problems with response 2 and it highlights some problems with the Kuzari Principle. First, not all witnesses to the events on October 13,1917 claim anything supernatural happened. In other words we have competing mass claims. Secondly, imagine this event happening over 2000 years ago. The believer’s story gets recorded, have reason to tell their children and authorities may have reasons to perpetuate the story. While dissidents are forgotten, leaving the impression all agreed a Miracle occurred.
The third problem is many experts have offered natural explanations of what occurred on October 13,1917 and it is more reasonable to accept natural explanation than claims of miracles. In other words, we need not accept a mass of people claim as to what really occurred at an event and thus the Kuzari principle is flawed.