You are correct!
Sam is actually correct. Regardless of his knowledge, one who always guesses occasionally gets lucky.
A p-chart is based on a binomial distribution. A simple explanation would be that if one took many samples from a binomial distribution and created a sampling distribution of these p-values, then:
a) The mean of the sampling distribution would be equal to the mean of the population.
b) That distribution will follow a normal distribution.
c) The standard deviation of the p values can be estimated by:
As you know, control limits are three standard deviations above the process average and three standard deviations below the process average. Thus, Sam Francisco accidentally sailed into safe harbor, saved by Lady Fortune herself.