If the sounds went throughout all the earth as
Romans 10:18 declares, then one can ascertain that as churches go astray, the Gospel message had gone astray as well. That is why those that love Him will keep His words and do them so that they may be found abiding in Him by faith in the grace of God. There can be no other gospel, so it is the keeping of the faith which is the good fight.
On the Day of Pentecost, many visiting Jews from other countries heard the Gospel in their native language and some believed, took that Good News back to their country. Scriptures can attest to the spreading of the Gospel there.
Although it cannot be confirmed about reports of Jesus appearing to the native American Indians, it stands to reason that wherever the Gospel message was received, it had gotten lost along the way, just as easily as an organized church can lose her way through the course of time.
Those that loved His words, kept them, having them written down out of love for the brethren that came after them, but even then, as scriptures also testify, there are many that will misapply scriptures in their walk with Him as given in "The History of the Keeping of His Word" thread.
So it may be odd that explorers may find that these people in farway places got it wrong, but only because the written word exposes the error since the gospel message doesn't change for there is no other gospel.