On the other hand, there's a strong indicator that there is substantial non-independence: lots of cities down the West coast set a record at about the same time

On the other hand, there's a strong indicator that there is substantial non-independence: lots of cities down the West coast set a record at about the same time, about 33-35 days ago. Also, what the visualisation doesn't show is the longest per-state time since a record. If they're all also on the order of a year, that's a strong signal that records are increasing. If that time varies randomly between now and decades ago, it's a sign the results are more random than trending.