Yes, that's exactly my point. Saying that it really supposed to be the probability of the data assuming the null hypothesis is true is pretty confusing to most

Yes, that's exactly my point. Saying that it really supposed to be the probability of the data assuming the null hypothesis is true is pretty confusing to most people and often times the gut feeling people keep us that it still somehow tells you how likely it is that the null hypothesis is true. I just like this example because it highlights that there is a distinction between these two probabilities.