Andrew Jackson not a "true" American?

I was browsing through the book "Military Commanders: The 100 Greatest Throughout History" for young readers, and in the entry about Andrew Jackson, it says that even though it's widely assumed that he was the first U.S. president born in a log cabin, it's likely that he was born aboard a ship bound for America from Ireland. He supposedly maintained that he was born on American soil, somewhere between North and South Carolina, in order to be eligible to run for the presidency!

This being news to me, I immediately turned to Wikipedia, w/c has no mention on it. A page turned up by Google points the source of this assertion to Allan W. Eckert's book The Frontiersman. Published in 1967 by Little Brown & Co., it's now out of print and the library does not have a copy.

This is not like the Sally Hemmings story where you can get some sort of evidence for or against the hypothesis... Documents? They would have turned up by now. But it still amazes me how all those Thomas Jefferson biographers steadfastly maintained that it was impossible for a man as great as TJ to engage in "such" behavior... and then to have been ultimately proved otherwise.