When President Obama recently outlined steps to reduce gun violence, mental-health advocates applauded his proposal to spend $500 million to aid access to care for the mentally ill. Advocates, however, are divided over whether proposals to ease the sharing of information with the FBI’s background-check system breach patient rights.

One change at the center of the debate involves a new rule from the Department of Health and Human Services that makes it clear that health agencies and medical facilities can report the names of certain people to the federal database without violating privacy laws. Another is a push by the White House to get the Social Security Administration to share with the FBI the names of mentally ill beneficiaries who do not manage their own affairs.

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Some mental-health advocates say such steps unfairly target the mentally ill, who are responsible for only a small proportion of gun violence in the United States. More often, they say, the mentally ill are victims, not perpetrators, of gun violence.

“These proposals . . . convey a pretty damaging message” to those with mental disorders, said Jennifer Mathis, deputy legal director of the Bazelon Center for Mental Health Law.

The White House, however, maintained that the HHS rule merely clarifies the federal health privacy law, known as the Health Insurance Portability and Accountability Act (HIPAA), by making it explicit that health agencies are allowed to share the names of those who already should be in the FBI database.

Frank Benenati, assistant White House press secretary, said the administration has “consistently fought to remove the stigma around mental illness and treatment,” while seeking to keep guns out of the hands of people barred from having them for mental-health reasons. That means, he said, ensuring that “appropriate records” are in the FBI’s National Instant Criminal Background Check System.

Under the Gun Control Act of 1968, people who have been involuntarily committed to a psychiatric facility, who are a danger to themselves or others, or who are unable to manage their affairs because of mental illness are prohibited from buying or possessing a firearm. The FBI keeps a list of these people, but the reporting of names by states and others is voluntary, and experts say the database is far from complete.

When mentally ill patients are committed by a judge, most courts report those names to the FBI because they are not covered by the HIPAA privacy law.

But health agencies and medical facilities, which are constrained by HIPAA, often do not report the names because they are worried about running afoul of the law.

The new HHS rule is directed at them, according to the administration, which also urged agencies and facilities to report demographic details such as height, weight, eye color and place of birth, to avoid misidentification. Clinical information is not to be shared.

“It basically is clarifying [that] you will not send diagnoses, just names,” said Paul Gionfriddo, president and chief executive of Mental Health America, a nonprofit, community-based advocacy organization for the mentally ill. “And that’s all this changes,” he said.

Gionfriddo acknowledged that removing a barrier to reporting will probably mean that more people will be added to the FBI background-check list, but he estimated that the number will be “hundreds, or in the single thousands,” and that the names are those “that should have been on the list anyway.”

Of greater concern, say others in the mental-health community, is the White House’s plan to propose a regulation that the Social Security Administration share information with the FBI. The Obama administration says that every year, about 75,000 people with mental-health issues are found legally incompetent and have records that could be shared with the FBI.

Although Bazelon’s Mathis said she understands the rule has not been written yet, she fears that it could broaden the criteria for inclusion on the FBI list, which was established under the 1993 Brady Handgun Violence Prevention Act.

She worries that people who are unable to manage their Social Security benefits for reasons other than mental illness will be included. “As far as I’ve been able to glean,” she said, “the proposal is not based on any evidence, or data, about gun violence by [these] people.”

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Gionfriddo countered that the wording in the Brady Act has always been open to interpretation, and that the potential impact of the rule depends on how it is written.

“We have to see what the language is,” he said. “It’s pointless to be alarmed about the future when we’re way at the beginning of a process.”