The first person mentioned, Carla Chavarria, is not a legal resident of the US, but she "obtained a two-year reprieve from deportation under the Obama administration's deferred action program." She does not have proper visa status. We are agreed on that.
Foreigners can own a US LLC, independent of their visa status. Therefore, she is allowed to own a US LLC. Owners of an LLC can draw money from the LLC. Therefore she can draw money from her LLC. Are we agreed upon that?
What then is the illegal part about the way that she makes money from the work that she does?
"most certainly do NOT say that a foreign person without proper visa status may form an LLC and then work here"
Since a foreign person without proper visa status may form an LLC, the key part is the "and then work here." I agree with you that her LLC is not a reason to let her stay in the country. She gets to stay in the country because she has a two-year reprieve.
In that case, starting an LLC is a way to make it possible for her to get money, based on her work as owner of the company.
So if "work" is broadly defined to include work done by non-employees (eg, owners), then she's legally making money from her work, no?
If not, then what law is being violated?