Things can come to mean something different from what their funders intend.
It happens all the time, especially with art, language and especially public monuments.
The Statue of Liberty’s connection to Ellis island is undeniable. The national museum of immigration is part of the same monument and run by the same staff.
It’s not ret-conning to say that the Statue of Liberty is indelibly linked - physically and symbolically - to mass migration of working and lower class people. It was the busiest port of entry for more than 60 years, and more than 20 million people entered there. There are uncountable contemporaneous accounts of immigrants viewing their passing the statue as a marker of the end of the voyage, and the beginning of their life in America.
One French guy funded it for one reason. 20 million others saw it as a symbol for something different in their lives.