My main objection was regarding the iffy sentence that "the probability that i(D) contains m is x%", as opposed to, say, you would expect "x% of those randomly

My main objection was regarding the iffy sentence that "the probability that i(D) contains m is x%", as opposed to, say, you would expect "x% of those randomly generated intervals to contain m". But, fair enough, I appreciate your sentiment about 'terseness'. One can only be so nitpicky with words when trying to communicate, before starting to sound like a criminal defense lawyer ...