Did you even read the link provided?  I sure hope you don't do your own taxes.  
A refundable tax credit in many cases gives money to people who have not paid any income tax.  A perfect example of that would be a single mother with 2 children who worked part time for minimum wage.  When she files her return, she claims head of household, takes herself and her two children and claims the EITC (Earned income TAX CREDIT)  The amount of money she will get back is MORE than she paid in.  It is a REFUNDABLE CREDIT ... 
keep insisting you are right ... and you will continue to look foolish