Washington (CNN) -- Immigration officials will not swoop in to deport a woman whose daughter asked first lady Michelle Obama about "taking people away" if they don't have proper paperwork, a Department of Homeland Security spokesman said Thursday.

Immigration and Customs Enforcement investigations are based on "solid law enforcement work and not classroom Q and As," said DHS spokesman Matt Chandler. Immigration and Customs Enforcement is a part of DHS.

The statement comes after a student concerned about her mother's legal status asked the first lady about the president's immigration policies Wednesday.

"My mom said, I think that she says that, Barack Obama is going to take away everybody that doesn't have papers," the young girl told Mrs. Obama as she visited a Washington-area school with Mexican first lady Margarita Zavala.

The unscripted moment was sandwiched between examples of Michelle Obama's signature policy initiatives -- a lesson on healthy eating and an exercise session -- and forced the first lady to walk the fine line of immigration reform policy language.

"Yeah, well, that's something that we have to work on, right? To make sure that people can be here with the right kind of papers, right? That's exactly right," she said.

The girl replied, "But my mom doesn't have any."

"[W]ell we have to work on that; we have to fix that and everybody's got to work together in Congress to make sure that happens. That's right," Obama said before moving to the next question.

Dana Tofig, a spokesman for Montgomery County, Maryland, schools, said the district would not identify the student and does "not ask about the immigration status of our students and their families."

"There was a Supreme Court decision that makes it clear that if there's proof of residency in the county, then we educate the child," Tofig said.

"And we're not going to identify the student or her parents. We protect the identity of our students."

Immigration took center stage in Washington on Wednesday as the president welcomed his Mexican counterpart, Felipe Calderon, to the White House.

Both leaders used the occasion -- the fourth time they have met for bilateral talks -- to take sharp aim at Arizona's controversial new law meant to crack down on illegal immigrants.

Calderon characterized the measure as discriminatory; Obama called it a "misdirected expression of frustration."

Obama also repeated his call for a comprehensive immigration overhaul.

CNN's Charles Riley contributed to this report.