Story highlights Jahi McMath's uncle says the family still hopes to move her to another facility

Terri Schiavo Life & Hope Network says it's trying to help move Jahi

Oakland hospital where Jahi now lies calls the McMath family claims untrue

She'll be kept on machines through 5 p.m. January 7, under a court order

The family of Terri Schiavo has joined the battle over Jahi McMath, a 13-year-old girl on a ventilator who has been declared dead by doctors.

"Together with our team of experts, Terri's Network believes Jahi's case is representative of a very deep problem within the U.S. healthcare system -- particularly those issues surrounding the deaths of patients within the confines of hospital corporations, which have a vested financial interest in discontinuing life," the Terri Schiavo Life & Hope Network said in a prepared statement.

The organization said it has been overseeing the efforts of several groups to help get Jahi transferred out of Children's Hospital Oakland and brought "to a safe place."

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Jahi's family said Tuesday it had found a facility in New York willing to take her. The Oakland hospital "refused to agree to allow us to proceed in that matter," Jahi's uncle Omari Sealey said.

The hospital denied the accusation.

"We have done everything to assist the family of Jahi McMath in their quest to take the deceased body of their daughter to another medical facility," hospital spokesman Sam Singer said.

"To date, they have been unwilling or unable to provide a physician to perform the procedures necessary, transportation, or a facility that would accept a dead person on a ventilator. Our hearts and thoughts go out to them in this tragic situation, but the statements being made by their attorney and some family members are misleading and untrue."

Family attorney Christopher Dolan had accused the hospital of being "hell bent" on ending Jahi's life.

A judge has declared Jahi brain dead as well. Doctors say there's no chance she will come back to life.

Omari Sealey, Jahi's uncle, said Wednesday that the family still hopes to move her to another facility.

He accused the hospital of starving his niece by not using a feeding tube to provide her with nutrients.

Singer said a judge Tuesday had dismissed the family's request for additional medical procedures, including a feeding tube.

A deadline loomed Monday as a judge had said the hospital could disconnect the machines after 5 p.m. (8 p.m. ET). But shortly before Jahi could have been cut off, that same judge extended his order to 5 p.m. (8 p.m. ET) on January 7.

Terri Schiavo died in 2005, nearly two weeks after doctors removed the feeding tube that had sustained her for more than a decade. She was severely brain damaged and became a national focal point in the right-to-die battle.

Her husband and guardian, Michael Schiavo, said she wouldn't have wanted to live in her condition, which Florida courts deemed a "persistent vegetative state." Her parents fought to have her kept alive.

"Persistent vegetative state," however, means the brain still has some activity, even though the patient is in a deep state of unconsciousness. Another word for this is "coma," according to the National Institutes of Health.

Schiavo's parents, brother and sister created the Life & Hope Network.

The statement Wednesday about Jahi included a quote from Bobby Schindler, Terri Schiavo's brother and executive director of the organization.

"Families and individuals must make themselves aware of what so-called 'brain death' is and what it is not," he said.

"Every person needs to understand that medical accidents happen every day. Families and individuals must be more aware of the issue of accountability and patient rights."

Last month, Jahi had surgery to remove her tonsils, adenoids and extra sinus tissue. Doctors had recommended the surgery to treat pediatric obstructive sleep apnea, a condition that made her stop breathing in her sleep and caused other medical problems.

Before the surgery, Jahi said she was worried that she would never wake up, according to her uncle. She seemed fine after the surgery and asked for a Popsicle because her throat hurt.

It wasn't long before something went terribly wrong. In the intensive care unit, the girl began bleeding profusely -- an image that her mother told CNN would be forever seared in her mind.

According to family members, Jahi went into cardiac arrest. Days later, she was declared brain dead.

Hospital officials have said privacy laws prevent them from discussing details of the case.