It's true. There's a whole Planet Money episode about this somewhere in their archives; I think Economics Explained on YouTube also touches on this. Shell corps are the way to go (not that I would know, of course).
Episode 390: We Set Up An Offshore Company In A Tax Haven
It's been a long time, but remember thinking how well done it was. TLDR was (as previous poster mentioned) that Delaware corps were best for anonymity.