All scripture is interpreted by its readers, and these verses are open to multiple interpretations. Historically, they have been interpreted as indicating that only the people mentioned in the Book of Mormon, the Lehites, Mulekites, and Jaredites, were the only ones who came upon the land. That is a very simple reading of the text, but one which falls before the evidence of history and archaeology.
Lehi spoke in a land that was already inhabited. How do we know that? We know he landed on a coast, and there was no habitable coast in the entire hemisphere that did not have some human population. There were numerous people who had already come to the New World before any Book of Mormon population arrived. Even the early Jaredites probably arrived on a coast where they could have been met by existing populations.
Then again, if there were already people here, perhaps they were included among those Lehi indicated that the Lord would bring. The Jaredites were already in the land, so that promise of whom the Lord would bring was not exclusive to the future.
It is therefore difficult to know how this prophetic statement is to be reconciled. Inside the text of the Book of Mormon, the conditions of liberty were constantly under Lamanite attack, and often threatened by internal dissent. It is probably best to read these verses for the part that Lehi emphasized—the promise of protection upon righteousness—rather than emphasize the more problematic understanding of who might be brought, and from which nations they would be hid.