However, the man behind that legend is a lie.
I've said it before but this is nonsense and not implied by the game at all. It's a poor excuse with no legs to stand on, just like all the others.
Big Boss was a legend already, there are no lies. He did all the things that made him a legend and his progression as a legend was already depicted, from his impossible mission in Snake Eater, to his realization that he's a natural leader who resolves to direct his own fate, to a legendary commander ready to literally take on the world without allies with a firm ambition and concrete dream for the world itself. Big Boss still continues being a legend by intervening in conflicts globally even after Venom Snake wakes up, making Venom Snake utterly pointless because Big Boss was putting himself in the very situations Venom Snake was created to prevent.
Venom Snake did
nothing worth noting, none of his exploits are conveyed, mentioned or hinted at by later titles. He contributed nothing to the legend of Big Boss. The legend the characters of the series and we the players ourselves hear about does not involve Venom Snake at all. We've heard of Big Boss' exploits in Russia, Mozambique, Columbia, Costa Rica, Cuba, Kuwait, and so on. Nothing about Afghanistan or Angola, because nothing that happened there mattered to later events or even remembered by anyone directly involved in them. Ocelot and Miller are complete opposites of their established personalities.
If Kojima wanted to deconstruct the legend of Big Boss, he would've shown us his exploits that have actually been mentioned in passing throughout the series. Instead, we get a completely throwaway and utterly inconsequential series of events that explain nothing and add nothing. Liquid mentions in MGS1 that Big Boss belittled him as inferior, but he never met the real Big Boss and not even Venom Snake actually said anything to him of that nature, instead quite the opposite.
Kojima just wanted a twist for the sake of a twist. It's hard to decipher the motivation behind it because there was none, no explanation makes sense because the twist wasn't a natural progression of any plot points. It was shoehorned in for the sake of a cheap shock factor. In the end we're left with a story that is of absolutely no consequence to anything else in the series, with Portable Ops and Peace Walker having far much more immediate relevance.