Lott's false claim about Cummings' paper

The Fox News story that Lott cites contains some other falsehoods:

For several years, gun control advocates have been quoting a study that reached a very different conclusion. University of Washington doctors claimed that in a dozen states which had safe storage laws, 39 children's lives were saved.

But the study has been widely discredited because the researchers never factored in that accidental gun deaths have been falling everywhere for decades.

The author of the article does not say where he got the claim that the study was "widely discredited" because they didn't factor in national trends, but presumably it was Lott since Lott says something similar on page 313 of The Bias Against Guns:

The Cummings et al. (1997) research provides evidence of a 23% drop in juvenile accidental gun deaths after the passage of safe storage laws. Juvenile accidental gun deaths did decline after the passage of the law, but what Cummings et al. miss is that these accidental deaths declined even faster in the states without these laws. While the Cummings et al. piece examined national data, they did not use fixed year effects which would have allowed them to test whether the safe storage states were experiencing a drop relative to the rest of the country.

However, the study did in fact control for national trends and it did use fixed year effects and it did test and find that the safe storage states were experiencing a drop relative to the rest of the country. From the study:

To control for national trends over time in firearm mortality rates, all states were included in the analysis, and 15 indicator variables were used to represent each calendar year. Categories of age, sex, and race were examined as potential confounders.