Did non-pharmaceutical interventions actually help against the Spanish flu?

From three economics Ph.D students at Harvard, namely Andrew Lilley, Matthew Lilley, and Gianluca Rinaldi:

Using data from 43 US cities, Correia, Luck, and Verner (2020) find that the 1918 Flu pandemic had strong negative effects on economic growth, but that Non Pharmaceutical Interventions (NPIs) mitigated these adverse economic effects. Their starting point is a striking positive correlation between 1914-1919 economic growth and the extent of NPIs adopted at the city level. We collect additional data which shows that those results are driven by population growth between 1910 to 1917, before the pandemic. We also extend their difference in differences analysis to earlier periods, and find that once we account for pre-existing differential trends, the estimated effect of NPIs on economic growth are a noisy zero; we can neither rule out substantial positive nor negative effects of NPIs on employment growth.

I am very willing to publish a response from the original authors on this one.