Yes, it is true. The bars and the term moustache have been around for quite a while. I have owned an 1890s Dayton racer that had them and my 1878 Rudge hi-wheel that I posted the YouTube has them. They were made initially to give clearance for a riders knee in the case of the hi-wheel bike. You see, since it is a direct drive ( I won't say fixie for obvious reasons )the pedal stroke drove your knee directly up under the handlebars. If you did not have the proper clearance then you either bent the handlebars, broke your leg or fell over. This is from a time when bike sizing was real important.
Ray Homiski
Elizabeth, NJ