It would make sense if Rolex published that advertisement after purchasing Aegler Uhrenfabrik in around 1914 (which was then renamed Aegler SA, Rolex Watch Company). It's not so much of a lie, more a slight exageration. Yes, the company that made the movements was founded in that year, which Rolex had purchased. It is also easy to look back on business practices from 100+ years ago with a modern eye and condemn them, where as how do we know this was not common business practice ?
It's not unlike some of the companies today that buy the rights to a watch brand and start producing watches under that name, while also claiming a history dating back to the 1800s.. it's simply not true, but they still do it.
Even Blancpain did this!