Very true. The real issue is that the wages often don't get "recycled" in the U.S. economy, but are sent overseas.
The Indian and Pakistani tennis team guys we played against last week, aren't spending their paychecks at Home Depot to upgrade their houses, since they live in apartments. For an anecdotal example.
I forgot to mention, offshoring manufacturing industries to China, OTOH, is worse than daylight robbery, and a major failure for the security of America, and every other nation that faces a Chinese threat.
However, we all want sub-$500 PCs and dirt-cheap electronics, for which we all might have to pay a dear price in the near future...
So, what about the taxes they pay, rent, food, transportation? How much do YOU save? That amount is what they say, approximately, and possibly send it oversees. It's a small percentage.
Most importantly, you do not take into account the product these foreigners produce, which would not be created at all in their absence. Your account for the impact on the economy is very incomplete.