Spot on. Immigration to America is a privilege, not a right. The same holds true for non-immigrant visas.
My wife is an immigrant. When she came to the US in 1969, she was told that coming to America was a privilege, not a right, and if she wanted to work and be a productive citizen she was welcome, but if she went on welfare, or committed a crime, or in any way became a burden on society, she would be immediately deported.