Republican presidential candidates who want to deport undocumented immigrants en masse, end birthright citizenship, and build a wall along the Mexican border just got some new ammunition. A report released Wednesday by the Center for Immigration Studies, an organization that advocates for reducing immigration to the United States, has concluded that 51 percent of households headed by immigrants—legal or undocumented—receive some kind of welfare. “They are creating a significant burden on public coffers,” writes Steven Camarota, the study’s author and the director of research for CIS. “By using welfare programs immigrants may strain public resources, harming taxpayers and making it more difficult to assist the low-income population already in the country.”

While that sentiment is likely to resonate with conservatives, the facts prove otherwise: Native-born Americans aren’t footing the bill for immigrants so much as immigrants are contributing to a welfare system that many of them can't take advantage of.

The Personal Responsibility and Work Opportunity Reconciliation Act of 1996 cut back on welfare extended to immigrants. It categorized green card holders and refugees granted asylum as “qualified,” and all other immigrants—including undocumented workers and many people lawfully here in the United States—as “not qualified” and therefore ineligible for welfare. But the law stipulated that even qualified immigrants had to spend five years in the United States before they could apply for benefits like Medicaid, food stamps, or cash assistance for families with children. Since that major welfare reform, some states have responded by providing for immigrants with programs that offer health care to the children of immigrants or pregnant mothers, and a few states—like California and New York—offer nutritional or cash assistance. But those efforts are mostly limited to qualified residents, while all other immigrants are still almost universally banned from receiving welfare.

The CIS study exaggerates the number of immigrants on welfare by using households as the unit of analysis; as long as the head of household is an immigrant, they consider it an immigrant household, and Camarota counts a household “as using welfare if any one of its members used welfare during 2012.” This means that a household with an American spouse who therefore qualified for welfare could be counted as “using welfare.” The same would go for a child born in the United States to immigrant parents. If he or she received subsidized lunch at school, the whole household would be categorized as “using welfare.” As the Cato Institute notes in its critique of the study, that measure is “ambiguous, poorly defined, and less used in modern research for those reasons.” Relying on such mutable methodology let Camarota exaggerate the number of immigrants on welfare to back up the claim that Americans are footing the bill for immigrants.

Groups like The American Immigration Council have long argued that, contra conservative depictions of “moocher,” immigrants have long given more to the welfare system than they take from it. “In one estimate, immigrants earn about $240 billion a year, pay about $90 billion a year in taxes, and use about $5 billion in public benefits,” a 2010 report by the Council found. “In another cut of the data, immigrant tax payments total $20 to $30 billion more than the amount of government services they use.” And a report by the U.S. Chamber of Commerce in 2013 found that “more than half of undocumented immigrants have federal and state income, Social Security, and Medicare taxes automatically deducted from their paychecks.” Those immigrants are essentially helping to underwrite the welfare system, providing an enormous subsidy to it every year without being able to reap any of the benefits.