This hypothesis is wrong. It also violates the acceptd rules of Natural Selection from Darwin. The scientifically correct explanation from computational cognitive neuroscience is here. The human language organ in the brain has nothing to do with lying except it provides an empirical window on how any animal neocortex computes. That includes deceit but most important language is what makes us unique...not our "intelligence". We can communicate about what our brains compute. No other animal has this capacity with such fidelity.

https://medium.com/liecatcher/the-natural-evolution-of-human-lies-655e983ee6c6