Story highlights The woman's family confirms her identity, human rights groups say

18-year-old left home in July, didn't come back; activists said security forces killed her

"I am now alive and not dead," a woman who says she's Alhusni now says on Syrian TV

Amnesty International says this shouldn't obscure the "big picture" of abuse

Zainab Alhusni, the young woman reportedly slain and mutilated while in Syrian custody, appears to be very much alive.

A young woman appeared on Syrian TV on Wednesday and identified herself as Alhusni, whose reported mutilation stirred outrage and condemnation across the world, long angered by the tough government crackdown against protesters there.

Her family confirmed that the woman on TV is indeed Alhusni, but they have not yet been able to speak to her, Amnesty International and Human Rights Watch said in a joint statement.

"I saw on TV that security forces detained me and burned my body ... and that they cut it up and handed it to my parents," said the woman, who resembles pictures of Alhusni obtained by CNN.

After that, the woman, who is from the restive city of Homs, said she decided to tell authorities the "truth."

"I am now alive and not dead," the woman said on TV.

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Several sources told CNN last month that the 18-year-old woman had stepped away from her home in July to buy groceries and was whisked away by Syrian security forces to coax the surrender of her activist brother, Mohammed, who often led demonstrations against embattled Syrian President Bashar al-Assad. A neighbor, activists, and human rights groups said she ended up beheaded and dismembered.

They said the woman's family reported her body had been returned to them by the government.

The family held a funeral and buried the body, Amnesty International and Human Rights Watch said.

The groups issued a statement saying they regret any inaccuracy in the misidentification of the body as that of Alhusni, and that both organizations regularly verify their information with multiple and independent sources.

Amnesty International said it had spoken directly to one of Alhusni's brothers to confirm the death, and Human Rights Watch later interviewed the woman's mother as well as a brother who washed the corpse prior to burial.

"It now appears that Zainab's family misidentified the body that was presented to them due to the extensive damage to the body," the groups said.

In the Syrian TV interview, the woman said she left home without telling her parents and went to live with relatives about five days before Ramadan, which would have been in late July. She said her parents didn't know she is alive.

"I ran away because my brothers used to torture me and beat me. That is why I left," she said.

She said security forces never detained her or raided their house.

"I want to tell my mother to forgive me and be pleased with me," she said.

Alhusni's family members couldn't be reached by CNN for comment.

Amnesty International said the TV interview clearly raised questions about information it released last month on Alhusni's death and the discovery of a body at Homs Military Hospital.

"The identity of the murdered female victim buried by the Alhusni family remains unknown and Amnesty International and Human Rights Watch called for an independent investigation to reveal her identity," the groups said.

Neil Sammonds, Amnesty International's Syria researcher, said it is important that the issue not obscure the larger problem of widespread abuse, including the deaths of dozens of detainees over the year.

"The big picture is that all sorts of horrendous abuses are going on," Sammonds told CNN.

Sources who reported Alhusni's death told of a chilling sequence of events after her disappearance.

Several days after she went missing in July, security forces called the family and offered to meet them in a pro-Assad neighborhood, where they would trade Alhusni for her activist brother.

On September 10, the family says, Mohammed was wounded in a demonstration. He came back to his loved ones a corpse. The family believes he was tortured to death.

In a statement posted to YouTube, another brother, Yousif Alhusni, describes multiple gunshot wounds to Mohammed's chest and a single shot through his mouth.

The family went to collect Mohammed's body from a hospital when doctors told them another unclaimed body with the label "Zainab Alhusni" had been kept in the morgue's freezer for some time.

When the family received the body, the head and arms had been chopped off. Chunks of the body's flesh were charred, appearing in places to have been melted or burned down to the bone.

Authorities forced Zainab Alhusni's mother to sign a document saying her daughter and son had been kidnapped and killed by an armed gang, Amnesty International said in an online statement.

Asked why she chose to appear on TV, the woman claiming to be Alhusni said, "Because one day, I will get married and bear children, and I will need to register them."