No one in American history is a "real American" unless everyone is. Everyone came here from somewhere else at some point. To pretend you are using some objective criteria to determine this is just a shroud for bigotry. Who made up your All American roster in 1630? All those pasty WASPy people were newcomers back in the day.
As for BYU, Mormonism was born in the United States and has a story that puts Jesus on the continent; it is the most "American" of any religion.