U.S. nationals and permanent residents can get EITC to supplement low wage income. Letting in more illegal aliens that will compete with them in the labor market is absolutely a policy choice - it has zilch to do with "market dictates". If you don't allow illegals into the country, the market will thereby be allowed to "dictate" higher wages.
The premise of the comment that you are responding to is that because of supply and demand, and because these people are desperate, it reducing the wages for those jobs and makes those bad jobs worse.
Thats horrible and less people should be doing those bad jobs, and the wages should increase! Desperate immigrants doing those jobs is just people pushing off bad things to a vulnerable population, and the world would be better off if those jobs got automated away entirely.