You actually have it backwards. US firms that do a lot of business overseas are being paperwork-shifted outside of the US not to avoid paying taxes on US operations but to avoid paying US taxes on operations that take place largely overseas.
This is how Apple ends up with 250 Billion (or whatever it is now) overseas that it doesn't want to Repatriate and pay US taxes on. That money wasn't earned by selling iPods in the US, it was earned by selling iPods everywhere else.
The first is the US government not doing enough to prevent shell IP licensing from being used to eliminate US profits (while the companies are benefiting from US stability and legal protections).
The second is the issue with US companies repatriating (or not) profits earned in foreign subsidiaries.
This is how Apple ends up with 250 Billion (or whatever it is now) overseas that it doesn't want to Repatriate and pay US taxes on. That money wasn't earned by selling iPods in the US, it was earned by selling iPods everywhere else.