[bradleyjg]

They don’t. Suppose I incorporate a company in Grand Bahama “Shell” and fund it with $10,000. The company turns around and buys $10,000 worth of Apple stock. A year later, Apple has doubled and I sell my company Shell to my friend John. If John and I are both non-Americans then the US taxing authority will never hear about this transfer or be able to tax the capital gain.

[valuearb]

So you and your friend John are foreigners investing foreign capital in the U.S. company Apple. Why do we want to use the tax system to discourage this?

[Erlich_Bachman]

To realize that gain you actually need to sell the Apple stock. It would be perfectly possible (as I am proposing) and viable to make that transaction be forced to go through US. You could still sell the "Shell" to someone without US knowing about it, but once you actually would want to do something with that gained money - you would need to sell the underlying stock and deal with IRS.