They're talking about this article from the Telegraph that catalogs complains about changes in American accounting and withholding rules for British banks that contract with the IRS. (If you're curious, the proposal is on pages 41 and 42 of the administration's tax green book.) What I find impressive is that, while these rules might impose additional administrative costs on banks, they have nothing -- really, absolutely nothing -- to do with investors 'pulling out of American markets,' much less 'free trade.' The rules are entirely about getting Americans with accounts and investments abroad to pay taxes that they are already legally obligated to pay. There might be some practical disagreement about the best way to go about doing this, but as far as know no one makes a serious argument for why we shouldn't be enforcing existing US tax obligations. Plenty of unserious arguments, though.
Tax Cheats is certainly one big facing issues to be solved by the presidents, by recovering these source of capital.
"no one makes a serious argument for why we shouldn't be enforcing existing US tax obligations"
Are you saying that cost is no object? I don't know the cost/benefit analysis for this particular case, but in general, we should consider the cost as well as the theoretical goal of any proposals. When the administrative burden gets high enough, foreign banks will simply refuse to deal with US citizens.
When I lived in Hong Kong in the 1990s, most (or, as far as I know, all) brokerages wouldn't allow US citizens to open accounts, because they didn't want to go to the trouble of worrying about IRS reporting. They also wouldn't knowingly send research reports to Americans out of concerns that the US SEC would get upset over lack of consistency with US reporting standards, etc. So, the average US citizen living there was simply shut out, because of the administrative costs imposed.
As for discouraging foreign investors from investing in the US, have you looked at the procedures imposed for proving whether or not any investments are actually by US citizens? Perhaps every single investment by foreigners in the US will become subject to extensive reporting requirements, on the off chance that a US citizen is trying to disguise herself as a foreigner. Wouldn't a substantial increase in costs tend to discourage investment?
The underlying philosophy here is that any income you make, even if it was earned in a foreign country, while you were overseas, with absolutely no support from the American government, society or economy, is still subject to American tax.
Because we own you, and you owe us.