One theory that is being floated on Reddit runs like this:
Kleiman is Satoshi, and had the keys to the ~1 million bitcoins. He dies, and his USB stick/computer/whatever went to a relative, who doesn't realize what he is holding. Wright knew Kleiman and knew he was Satoshi. So he invents this crazy story about being Satoshi, but that he can't spend the coins because they are all in a trust that was held by Kleiman.
So now Wright comes public claiming to be Satoshi - and sets himself up to launch a lawsuit against Kleiman's relative to get "his" bitcoins back. If Wright pulls this off, he gains the fabled treasure of 1 million bitcoins off Kleiman's estate.
Thoughts pro and con?
I doubt it but it's a better theory than 99% of garbage being posted on this topic over the last couple of days. It's increasingly obvious that despite not being able to present actual cryptographic proof Wright is putting a lot of effort into obfuscation and trying to sway the public opinion, whether it's for his business interests or something else.