You need to learn about FICA. It is an income tax and is what the EITC rebates. Nobody has ever gotten EITC that hasn’t paid FICA taxes.
Learning is hard. However, my employer and I are painfully aware of the dark force known as FICA.
Regardless, my quote with which you seem to disagree came from your link. Here it is again:
"The EIC may lead to a refund even if no income tax was withheld or owed."