Found this page on BaseballReference.com. It shows how MLB runs scored per game, hits per game, batting averages, etc., have varied over the years.
I’m looking at these numbers, and yeah, runs per game were under 4 for most of the years between 1904 and 1919, but … were they down so far that they could say it was a dead ball era?
Also, there was a scene in Eight Men Out where the actor playing pitcher Eddie Cicotte was talking to a reporter about a new baseball that was wound tighter. After that year, runs per game went over 4 for the next 20+ years.