As I understand it, you can't own a company that you(or a relative) own a controlling interest in with your IRA. I can see the sense in this because if own 20% the person(people) who own the other 80% have an incentive to make sure I'm not playing any kind of games with the finances.
In the case of Thiel, it seems like he took $2000 and made a moonshot investment in Paypal. At that point his investment could have just as easily went to $0 as it was to hit $5 billion. He took the risk, why shouldn't he have gotten the reward?