The phrase "No Human Being is Illegal" raises a legitimate point and issue. According to the Universal Declaration of Human Rights adopted by the UN in 1948, everyone has a right to their own identify, and to life. Therefore, to declare someone illegal, or under automatic suspicion of being illegal, because of their identity, violates these principles.
Behavior or actions can be declared illegal, but these can be committed by anyone. The phrase also likely refers to the ethical argument for unrestricted immigration - that there are jobs available for immigrant workers here, and people are moving here to escape economic poverty, so to deny them entry is to deny them economic sustenance, and therefore their right to exist on Planet Earth.
Global citizenship is an unrealistic dream, but we can realistically move closer to that and already are in some ways. In the European Union, citizens of many countries share the same rights and may travel freely within the zone with little or no identification. We also encourage a move towards global citizenship when we champion and practice economic globalization, because it removes economic boundaries between countries, and political ones become more transparent when that happens.
The problem with the Arizona law where this concept is concerned is that it empowers and requires law enforcement to verify citizenship, and allows them to ask for verification based on mere suspicion. Therefore, to be Latino in Arizona makes you an automatic suspect, while it is much less likely they will be profiling white male Canadians.