The Institute is formerly the Massachusetts Institute of Technology (AKA MIT). I don't know much more than that, or even if there is enough info out there, but it was definitely there.
I don't see the idea of a frozen DNA bank nessicarily leading to the player being an android. Maybe they unfreeze you when you are next in line, expecting you to be dead but you're not. It seems a bit thin, but I think with some work it could fly.
However I would go with: The technology wasn't ready but Vault-Tec thought it was worth the risk, but only for one or a few vaults. If there is only a 10% (for instance) chance of success someone like Mr. House wouldn't take that risk, but it would be simple enough to lie to your average person and tell them it is low risk.
Cryogenicly freezing people would be the best way to ensure human survival, but if the technology isn't ready, and therefore unreliable, you couldn't use it on a large scale.
Though we still don't know if that is what we are getting, it based on a supposed leak.