Yeah… I don’t think there is actually good proof that something being illegal actually stops a meaningful number of things on its own. There are plenty of studies that people do things that are socially frowned upon less IN FRONT OF OTHER PEOPLE (say littering for example), but very weak evidence it stops such activity in any meaningful way in private settings. Likewise there is plenty of evidence that other forms of punishment (which is to say, no immediate social stigma) actually don’t really correlate with reduced activity at all.
Best guess? Just avoiding being sued. Something being a false statement is a matter of fact that’s easily proven. Something being a lie requires proving state of mind. In the US I can’t imagine actually winning such a suit, but its still safer to cover asses.