That's what the NYT told readers in an article reporting on the debate over Scottish independence. The article referred to a study by a Scottish engineering company, the Weir Group, that Scotland would incur $840 million in transactions costs if it were to adopt its own currency. This would be the equivalent of roughly $65 billion a year in the United States. Since many countries that have smaller economies than Scotland have their own currencies, it is difficult to believe they incur these sorts of costs. (Trading costs on most currencies are typically in the range of 0.01 percent.)
The article also said that Great Britain may not let Scotland keep the pound if it were to become independent. Actually Great Britain really doesn't have any choice in the matter. Any country can use any currency it wants as their official currency. Several countries (e.g. Ecuador and Panama) use the U.S. dollar as their currency. They did not ask the United States for permission to do so.
The better question is why an independent Scotland would want to keep the pound as its currency. Presumably one of the goals of independence would be to free Scotland from the grips of the austerity policies being pursued by the conservative government. This would not be possible if Scotland remained tied to the pound, just as the euro zone countries cannot break from the path of austerity as long as they stay in the euro zone.
The piece also includes the claim, based on two studies, that:
"Creating a border with Scotland’s largest trading partner — the rest of Britain — could also be costly. Researchers at the University of Edinburgh and the University of Stirling project that such a change could reduce Scottish output more than 5 percent."
This implies an enormous cost to international borders. The implication is that Canadians effectively pay a tax of roughly $2,000 per person per year because their country is not part of the United States. That doesn't seem plausible.