Why would Henry Gale spin a story that is demonstrably false?
He chose a false name connected to a corpse on the island.
There are very few things these Losties can verify, but one of them is the identity of Henry Gale. Wouldn't it make more sense to claim to be Harry Smith, adventurist, who crashed on the island with balloon partner Henry Gale, who died and is buried under a pile of rocks. For that matter, why not use your real name? It's not like he's Gary Hogeboom or anything.
And why the story about the wife? Was that to make him seem credible? The whole thing was weak from the beginning because anyone ballooning 1,000 miles out in the ocean would be surrounded by support aircraft.
A good con man requires spinning the info you have, not fabricating foolishness. So what is the purpose of the elaborate and dumb lie?