Nephi's vision of the events of the Restoration are clear enough that we must understand that in this prophecy Nephi is declaring the preservation of the record more than the literal handing from generation to generation. That handing down of the plates does in fact, occur for around a thousand years, and Nephi's prophetic understanding may or may not have included the length of time that the record would lie hidden from the world (though he is quite specific in other cases, such as the 400 years his people would last after the appearance of the Messiah in the New World).
For those peoples in whose hands the text of the plates was available, however, the words of those plates were a testimony to them, and a responsibility upon them to be judged by the words they had in their possession. This was true of the ancient Nephites and is true of the modern saints as well.