Everyone who works pays Federal taxes, no exceptions even for the poor.
That is false. Ever hear of the Earned Income Tax Credit? Millions of people get back more in their refund, sometimes substantially more, than they paid into the system every year.
That doesn't mean that they haven't paid Federal taxes. You need to be working and have taxable income in order to be eligible for the EITC.
And can you please provide a

for these "Millions of people get back more in their refund, sometimes substantially more, than they paid into the system every year."?
TYIA
Not everyone pays federal taxes and taxable income is not necessary to receive the Earned Income Tax Credit (EITC). I once worked for the IRS and I will explain how this happens with a simple example.
In 2014, a woman who filed as Head Of Household (HOH) with 3 children was entitled to a standard deduction of $9,100. Plus she was also entitled to a $3,950 exemption for herself and for each of her children for a total exemption of $15,800. Her standard deduction plus her exemptions totaled $24,900. Her taxable income was determined by subtracting this total from her Adjusted Gross Income (AGI); therefore, if her AGI was $24,900 or less she owed no taxes. All taxes withheld by her employer were refunded to her when she filed her return.
But there's more: Based upon her earnings of $24,900, she was also entitled to an EITC of $4,648. The EIC is a refundable credit which means this amount was added to her refund check.
As you can see, some people do not pay taxes. Plus taxable income is not necessary to receive the EITC. The EITC is not based upon taxable income but rather total EARNED income (some types of income, such as investment income, are not counted).
(NOTE: The IRS offers another refundable credit, the Additional Child Tax Credit but I'll save explaining that one for another time.)
Below are links to the 2014 Form 1040 and the 2014 EIC tables
http://www.irs.gov/pub/irs-pdf/f1040.pdf
http://apps.irs.gov/app/vita/content/globalmedia/earned_income_credit_table_1040i.pdf