The Founders were immigrants themselves. I don't get this US hang up about "immigrants" as it is probably the country most constituted out of immigrants whether they go back one or more generations back. It has long been a melting pot of different cultures, religions, etc. It's actually what gives the US the strength they have - a strength in diversity. Some immigrants were slaves, and others came from all the other continents.
In my own country, my family immigrated here back in the mid-1600's, but even that has become a debate about whether this should be my home country because my family originated from Europe, and not Africa. So the question really is when is one an immigrant, and when not?
And if so, how does anyone "go back" to a country they were never born in? They are not recognised as from that country, either. It's pretty complex.