> Since all outcomes are 0 or 1, and drawn with the same (unknown) probability, we know that the number of ones and zeros follows a binomial distribution. This means that the confidence interval of a “k out of n” scenario is a Beta distribution.

Pretty confused by this sentence. The mean of a bunch of 0s and 1s cannot follow a beta distribution. The support set is not continuous. I think the author is making Clopper-Pearson intervals, but dropping some terms.