Umm, again, those are shares of stock he owned as founder...not stock options.
In a startup that intends to go public and is courting venture capitalists, founders shares are options. They have a vesting schedule and a strike price and you have to purchase them with cash, which is exactly what Thiel and PayPal both said he did. For tax purposes, the value of an exercised option (or a purchased founder's share) is the FMV on the date of exercise, not the strike price.
If I start a company which issues stock I can put whatever valuation I choose on those shares.
Sure, you can set the initial value however you want, but once you sell shares to outside investors the fair market value is set by how much they are willing to pay.
I really don't know if Thiel did anything wrong here. I'm just trying to explain the argument. It's possible that ProPublica has it wrong and the fair market value of his PayPal stock was only $1700 on the day he acquired it and any rational person would have agreed with that valuation on that day. I've worked at a couple of early startups where the value of my stock yo-yo'ed all over the place if we even knew what it was, so I can easily believe PayPal also had some wild swings in the early days.
ProPublica has also connected a lot of dots that weren't available to the IRS when 1999 tax returns were filed, and hindsight is 20/20. If PayPal had gone out of business 6 months after Thiel bought these shares with his Roth IRA funds, we definitely wouldn't be having this discussion.