The person you are replying to isn't saying anything about the probability of individual events. They are talking about the probability of at least one of many events occurring, which does change with the number of events being considered
Indeed, but I think you might be misunderstanding what I said. Think of the universe as a nearly infinite number of dice rolls all independent and in parallel. Any possible rare combination of dice rolls will actually be happening constantly.
Right, but while it may only be a 1/6 chance that a single die roll will give you a six, rolling more and more dice eventually makes it a near-certainty that at least one will give you a six.