Potential 2016 Republican presidential candidate Ben Carson, who happens to be a retired neurosurgeon, raised the possibility that undocumented immigrants helped trigger the outbreak.
Unlike Chris Christie and Rand Paul, Carson has supported strict vaccination policies. But on Tuesday he said, "We have to account for the fact that we now have people coming into the country sometimes undocumented people who perhaps have diseases that we had under control."
Rep. Mo Brooks (R-Mo.) went even further. Asked during a radio interview whether there is a link between immigration and the measles, the congressman said there is no question "illegal aliens" who haven't received proper healthcare screening have brought diseases into the U.S.
"It might be the enterovirus that has a heavy presence in Central and South America that has caused deaths of American children over the past six to nine months," he said. "It might be this measles outbreak. There are any number of things."
In fact, the likelihood that the outbreak was caused by an undocumented immigrant is very small.
The largest measles outbreak in recent U.S. history occurred last year in Ohio, when an unvaccinated Amish missionary returned from the Philippines to a community with a low immunization rate.
The Southern California flare-up, which began in December, most likely did come from overseas. Officials at the Centers for Disease Control believe a foreign tourist or an American who contracted the virus abroad brought it to Disneyland. Testing shows the current strain of measles resembles those in Indonesia, Qatar, Azerbaijan, and Dubai.
Those nations are not in the top 10 countries of origin for undocumented immigrants in the U.S. And Brooks missed the mark when he said that "illegal aliens … have not been blessed with in their home countries with the kind of healthcare, the kind of immunizations we demand in the United States."
The home countries of most unauthorized immigrants have economic and security concerns that push their citizens to head north, but they do have childhood vaccination programs.
The measles immunization rate among 1-year-olds in Mexico, where almost six in ten undocumented immigrants were born, was 89 percent in 2013, according to the World Health Organization. That's down from 99 percent in 2012, but just two percentage points less than the United States' rate of 91 percent.
Honduras (95 percent) and El Salvador (94 percent) both had higher rates than the U.S., while Guatemala was at 85 percent. In total, 113 countries have higher measles vaccine coverage rates than the U.S.
Brooks also claimed that requirements for public school vaccination requirements had been suspended "to some degree" for undocumented students. While enforcement across the board has lapsed in some school districts, such as Maricopa County, Arizona, all 50 states require public school students to be vaccinated, regardless of immigration status, according to the CDC.
In the past, there have been vaccination gaps between white, non-Hispanic students and others. But a CDC study released last year showed no racial or ethnic disparities have been found in measles vaccine coverage since 2005.
The biggest factor fueling the measles outbreak isn't immigrants; it's people who have chosen to not receive vaccines for philosophical reasons, according to Dr. Anne Schuchat, director of the CDC's National Center for Immunization and Respiratory Diseases.
"It is frustrating that some people have opted out of vaccination," she told NBC News. "I think we do have some communities with many who have not received vaccines."
The state with the highest vaccine exemption rate, for both religious and philosophical reasons, was Oregon at seven percent, CDC data shows. In some schools in Orange County, California, 50 to 60 percent of kindergarteners are not fully vaccinated, The New York Times reported.
Jordan Fabian is Fusion's politics editor, writing about campaigns, Congress, immigration, and more. When he's not working, you can find him at the ice rink or at home with his wife, Melissa.