FamilySearch recently sent me a message telling me I had "X" number of ancestors who "emigrated from" British Colonial America. In fact, those ancestors "immigrated to" British Colonial America. Pretty embarrassing!
The issue is not the use of emigrate/immigrate. That email presumed that ancestors moved FROM British Colonial America TO the United States. In fact, they didn't move; the name of the place changed. The algorithm that was the basis for that little marketing email was poorly designed.