Dude, we're playing as a murderous gang leader turned multimedia icon turned President of the United States fighting aliens inside of a virtual simulation. Any logic surrounding Gat's "death" shouldn't be taken so seriously.
"Jean and Emma are not trained killers. I fear nothing but failure." - Psylocke, X-Men Legends
I thought it was a fine reason. The game itself didn't spend a lot of time talking about it and basically was like "This is why Johnny is back. Yup. Now back to kicking ass!" I thought the simple, barely believable explanation humorously worked for a game like this.
It's Saints Row. A series that makes you shoot zombies, aliens and even hooker assassins - while possibly having your main character look like a walking toilet or blow up doll. Seriously, who cares how believable Johnny's death retcon was? At least he's back!
"In a world without gold, we might have been heroes" ~ Assassin's Creed IV: Black Flag