Seems correct. A CI [a,b] means: “IF the parameter would be between a and b, THEN these data would not be significantly different”.
Or more simple: “if the real value would be somewhere around zero, then this sample would be quite normal and to be expected. But we have no idea what the real population value is, because all we have is this sample.”
This in contrast to bayesian logic: “based on previous knowlegde and logic, our best estimation of the population was … Now we have new data, which allows us to update our estimation”. Here the sample doesn’t contain more info neither, but we combine it with other information.