That's true ONLY IF America started to produce textiles. But the textbook trade models (e.g. Ricardian, Hecksher-Olin, etc) all pretty much recommend that America should just stick to producing fish and fur to maximise its gains from trade, and forget about a homegrown textile industry.
>But those of us who would be here would be pursuing our comparative advantage and exporting fish and fur. That's what economists tell you is right. Pursue your comparative advantage. That was our comparative advantage. We certainly wouldn't have had a textile industry. British textiles were way cheaper and better.
Comparative advantage allows for trade even when one country has an absolute advantage over another. Even if British textiles were better and cheaper than the American ones if America started to produce textiles it could make sense for the British to reduce their textile production if there are other goods they can apply the same resources to that have a higher value than they will pay for the American textiles they are now buying.
The wikipedia page is pretty good at explaining this:
http://en.wikipedia.org/wiki/Comparative_advantage