Excellent! I do believe that is what I have been saying all along. p has nothing to do with the content of the message, It has to do with the probability that the given message would be selected given a probability distribution of possible messages.
As such, H is not a measure of “information content” of a specific message. So what is H a measure of? Can we agree that H is a measure of something to do with the possible messages rather than the “content” of any particular message?
When someone writes -log p, that is a reference to the probability of a specific outcome -log pi. That’s the way I interpreted Joshua’s comment. Are you agreeing with my interpretation of his comment?