We receive this information through Ammon's report to Alma, which comes long after this particular exchange. It is doubtful that this information has any relationship to official Lamanite documents, if there were any. Thus the particulars of the exchange are likely to be Ammon's remembrances, and not an accurate word for word reporting of the original exchange. This does not make a serious impeachment of the text, only cautions us to remember the particular bias of the reporter.
In this case, we have Ammon declaring his desire to live among the Lamanites. This is tantamount to severing his Nephite relationship, and becoming Lamanite. Without some assurance that Ammon had no ulterior motive as a spy, it is unlikely that this declaration of a desire to live among the Lamanites would be taken at face value.