>That is what each of these statistical models did, yes. And the actual outcomes fell into these confidence intervals.
The CI is due to sampling error, not model error. If the error of the estimate is due to sampling error, the estimate should be randomly distributed about true value. When the estimate is consistently biased in one direction, that's modelling error, which the CI does not capture.
> If the error of the estimate is due to sampling error
What does "estimate" mean here? Gelman's model is a Bayesian one, and 538 uses a Markov Chain model. In these instances, what would the "estimate" be? In a frequentist model, yes, you come up with an ML (or MAP or such) estimate, and if the ML estimate is incorrect, then there probably is an issue with the model, but neither of these models use a single estimate. Bayesian methods are all about modelling a posterior, and so the CI is "just" finding which parts of the posterior centered around the median contain the area of your CI.
I'm not saying that there isn't model error or sampling error or both. I'm just saying we don't know what caused it yet.
The CI is due to sampling error, not model error. If the error of the estimate is due to sampling error, the estimate should be randomly distributed about true value. When the estimate is consistently biased in one direction, that's modelling error, which the CI does not capture.