What is the falsehood?    Poor people pay lots of taxes (why just focus on federal income tax).  And yes they do file and in some cases pay.  Why should they get an income tax credit?  Two simple reasons for those commenting here:
a) it is supported by the gospel and is at the core of our mission
b) US has built its values and principles upon redistributing wealth

Now, what you again get wrong - obviously, you have never studied who pays income taxes:

a) The vast majority of households that don't pay federal income taxes are either elderly or paying payroll taxes
b) Only about 7.9 percent of households are not paying any federal taxes at all. That's usually because they're either unemployed or on disability or students or are very poor.

These FACTS really do put your opinion in a negative context and show them to be lies.