All kinds of factual information makes the proposal look dumb. The article itself mentions that no-one knows if it's really the body of Leonardo da Vinci because "The church in which Leonardo was buried was destroyed after the French revolution of 1789. The remains were reburied in the castle’s smaller chapel of Saint-Hubert in 1874, beneath an inscription that describes them as 'presumed' to be the master’s." The stunt men also want to test the body to see if it's really Leonardo, claiming to know of "descendants," but there aren't any of those: Leonardo was very famous for being gay.
The reason why they think the Mona Lisa is a self-portrait is that they claim they know what Leonardo looked like (the famous "self-portrait" of an old man), and they claim they don't know who she was. Here are a few facts:
- The so-called self-portrait of Leonardo as an old man has never been definitively shown to be either by him or of him. It was discovered in the late 19th century and the identification as a self-portrait was at best wishful thinking. This painting is an essential prop for the dubious claim that Leonardo and Mona Lisa are the same face.
- Leonardo and many other painters of his time used conventions of proportion of faces which lead to exactly the type of similarities that are supposed to demonstrate that the Mona Lisa is a self-portrait. Computer merging of the two portraits looks convincing, but in fact a clever computer manipulator could make an equally convincing case for many other portraits if they were motivated. Again: wishful thinking takes over.
- There's actually solid evidence of Mona Lisa's identity as a specific historic person named Lisa del Giocondo. See this: Mona Lisa's Identity, Solved for Good?
Nicholas Turner, a former curator of drawings at the Getty Museum, said: “It sounds a bit fanciful, slightly mad, as if the Leonardo bug has taken hold too firmly in the minds of these people. We know that Mona Lisa was a specific person, she existed and it’s her portrait. If Leonardo heard about all this, he’d have a good chuckle.”For more debunking, see this neuroscientist's view of why Mona Lisa's smile is so mysterious: What is it with Mona Lisa's Smile?