This is but a half truth topic.

They are not eligible for "certain credits" as described above, however they are entitled to deductions, exemptions, and some credits which in turn do result in receiving more from a tax return than they had paid in through their taxes.

See publication 501 and 519 US Tax guide.

Pub. 519

Nonresident Aliens

You can claim some of the same credits that resident aliens can claim. You can also report certain taxes you paid, are considered to have paid, or that were withheld from your income.

Credits

Credits are allowed only if you receive effectively connected income. You may be able to claim some of the following credits.

Foreign tax credit.   If you receive foreign source income that is effectively connected with a trade or business in the United States, you can claim a credit for any income taxes paid or accrued to any foreign country or U.S. possession on that income.   If you do not have foreign source income effectively connected with a U.S. trade or business, you cannot claim credits against your U.S. tax for taxes paid or accrued to a foreign country or U.S. possession.   You cannot take any credit for taxes imposed by a foreign country or U.S. possession on your U.S. source income if those taxes were imposed only because you are a citizen or resident of the foreign country or possession.   If you claim a foreign tax credit, you generally will have to attach to your return a Form 1116. See Publication 514 for more information. Child and dependent care credit.   You may qualify for this credit if you pay someone to care for your qualifying child who is under age 13, or your disabled dependent or disabled spouse, so that you can work or look for work. Generally, you must be able to claim an exemption for your dependent.   Married nonresident aliens can claim the credit only if they choose to file a joint return with a U.S. citizen or resident spouse as discussed chapter 1, or if they qualify as certain married individuals living apart (see Joint Return Test in Publication 503).   The amount of your child and dependent care expense that qualifies for the credit in any tax year cannot be more than your earned income from the United States for that tax year. Earned income generally means wages, salaries, and professional fees for personal services performed.   For more information, get Publication 503. Education credits.   If you are a nonresident alien for any part of the year, you generally cannot claim the education credits. However, if you are married and choose to file a joint return with a U.S. citizen or resident spouse as discussed in chapter 1, you may be eligible for these credits. Retirement savings contributions credit.   You may qualify for this credit (also known as the saver's credit) if you made eligible contributions to an employer-sponsored retirement plan or to an individual retirement arrangement (IRA) in 2008. You cannot claim this credit if:

You were born after January 1, 1991,

You were a full-time student,

Your exemption is claimed by someone else on his or her 2008 tax return, or

Your adjusted gross income is more than $26,500.

Use Form 8880 to figure the credit. For more information, see Publication 590. Child tax credit.   You may be able to take this credit if you have a qualifying child.   A qualifying child for purposes of the child tax credit is a child who:

Was under age 17 at the end of 2008.

Is your son, daughter, stepchild, foster child, brother, sister, stepbrother, stepsister, or a descendant of any of them (for example, your grandchild, niece, or nephew).

Is a U.S. citizen, a U.S. national, or a resident alien.

Did not provide over half of his or her own support for 2008.

Lived with you more than half of 2008. Temporary absences, such as for school, vacation, or medical care, count as time lived in the home.

unless the person using it owns a business or is self employed, legally they can not use it in order to pay their taxes

I left that very confusing... the person using the ITIN must be a business owner or be self-employed, illegal aliens can not legally use it in order to pay thier taxes if they are working for someone else, they themselves must be a business owner or an Independent Contractor, for which they would receive a 1099-misc at the end of the year from the main contractors of whom they worked for.

I suggest Dave, instead of deleting my stance in regards to Mary, you had also better remove her accusations and assumptions in accusing me of something I have not done. I know you don't like that I am here, however you should be a little more even handed when it comes to these false accusations and assumptions which result in SLANDER. I also suggest you take it up with Mary and inform her that her situation is in dire straights with me. I expect and demand a PUBLIC APOLOGY.

Stop googling my name, stop posting comments using my name on other websites. If you went and checked out that website than obviously you keep googling information on me. Please, leave me alone.

I do not know you...all I know is that you have used my name on your own personal website. I called the main headquarters of that website and that account with my name posted on it is a privately owned account so I ask you one question. Since you have a reputation of following woman around on the internet...how what anyone have a way to know how far you would take it.

I am not blaming you but I want you to not use my name without my permission anywhere.

 Mary Spagetti?  If that's a real name, then I am not Wire Palladin.