The child tax credit applies to any of your children, your stepchildren, your foster children, your siblings, your stepsiblings, or any direct descendents of anyone listed so far, who meet the following criteria:
- you claimed them as a dependent on your tax return (which requires that you are the only person to claim them, they are a U.S. citizen or resident alien, and they do not earn enough income to pay for half of their own expenses)
- they are under 17 at the end of the year
- they lived with you for at least 1/2 the year.
The "loophole" here isn't that illegal immigrants are "allowed" to claim children living back in Mexico as dependents, it's that tax returns rely on the honor system, and the IRS doesn't have the resources to check them all. Some of these people probably do get audited and caught every year, despite the news report's assertion that the tax preparer guy never heard back from the IRS so the IRS must be doing nothing. In reality, the tax preparer guy wouldn't hear back either way, because the IRS is prohibited from disclosing any information about your tax return to anyone but you, unless you specifically fill out the part of the return that waives that privacy right. So the tax preparer guy would hear nothing back from the IRS whether or not they nailed any of the fraudulent returns he reported.