Maybe I can help, I do my own taxes each year and hopefully have a handle on some of this
Your basic tax exemption(if thats the right term) is only $9600. Basically if you made less than $9600 dollars you don't have to pay tax. The poverty line has no bearing.
A good rule of thumb if your in the lowest tax bracket would be to make sure 15% of your income is taken for taxes. It's not 100% accurate, but its a close, ballpark figure.
Basically your being taxed on $3100 of your income if you made $15,000. Going by my rough 15% ratio you would owe $450 dollars or so. They deducted $550 dollars, thus you get the difference back, in your case I guess $150 dollars or so.
The lowest bracket is generally that easy and the numbers you gave look right from my experience.(I've been doing my own taxes for like 17 years).
Now thats not to say that the tax collectors aren't bad people
or that they don't take too much money, but your numbers look right to me in simplistic form.