The phrase "undocumented" is bureaucratic speak for "you can't prove it."
"The allegations are undocumented."
In the context of immigration, one could say "she claims to face persecution in her country of origin, but this is undocumented."
That doesn't really apply to "undocumented immigrants," because it's usually not in doubt someone is an immigrant.
If their place of birth is unknown, and might be in the United States, you could use the phrase "undocumented immigrant."
I agree it's a propaganda phrase, and does not conform to clear English usage.
But "undocumented" does not mean something is sanctioned, it means it must be proven and has not been proven.