Who knows if it is true, or if anything anyone says about that family is true. There is so much "advocacy" and propaganda and just plain fantasy out there on the Internet. Heck, the same goes for newspapers like the New York Times.
To add to the lore, "Rothschild," which means "red sign" in mediaeval German, was supposedly adopted because of the sign he hung out over his store.
Which means that the name should not be pronounced "roths-child," but more like "rote-shildt."