Story highlights Syrian opposition officials say the moderate opposition didn't have Sotloff

Family spokesman: A rebel phoned ISIS and said Sotloff had entered Syria

Video of Sotloff's beheading came after another American was decapitated

Senators introduce a bill that would authorize a reward of up to $10 million

The family of slain American hostage Steven Sotloff believes ISIS paid as much as $50,000 to rebels who alerted the militant group that the journalist had entered Syria, a spokesman told CNN.

The family had learned from "sources on the ground" that a member of a moderate rebel group reached out to ISIS, Barak Barfi told CNN's "Anderson Cooper 360" on Monday.

"Somebody at the border crossing made a phone call to ISIS, and they set up a fake checkpoint with many people," Barfi said. "Steve and his people that he went in with could not escape."

Barfi said the tipster was one of "the so-called moderate rebels that people want our administration to support."

So how much was the tip worth?

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Sotloff's whereabouts were sold for "something between" $25,000 and $50,000, Barfi said.

'False' accusations

Sotloff, a 31-year-old freelance journalist, disappeared during a reporting trip to Syria in August 2013. Barfi said he last spoke to his friend the day he disappeared.

"Minutes before he was kidnapped, he called me from inside Syria to tell me that he was in," Barfi said.

Sotloff was supposedly turned over because his name was on a list of people responsible for a hospital bombing, his friend said.

"This was false. Activists spread his name around," Barfi told Cooper.

In fact, "Steve loved the Arab and Islamic world, and he wanted to bring their suffering to the world stage," Barfi said. "He believed that everybody was created equal, and the people in the Arab and Islamic world weren't terrorists, they were just people like you and me."

Who might have sold Sotloff out?

A senior administration official said there is no evidence to support the notion that Sotloff was in the custody of the moderate Syrian opposition at any time.

Syrian opposition officials, after consulting with their sources and activists on the ground, also deny the story.

But the Syrian opposition is made up of some 12 different rebel groups -- some moderate, some extreme, and some in between -- a key reason why U.S. President Barack Obama has resisted arming rebels in any significant way.

Was the beheading preventable?

The gruesome video of an ISIS militant decapitating Sotloff spurred international outrage at ISIS, the Islamist terror group that refers to itself as the Islamic State. The group is trying to establish strict Islamist rule over swaths of Syria and Iraq and has captured cities in both countries.

But that video wasn't the first time Sotloff was featured in an ISIS message.

Sotloff appeared in the earlier decapitation video of James Foley, another American journalist who was beheaded by an ISIS militant. In that video, which was released August 19, a militant said Sotloff's life depended on what Obama did next.

"Once Steve appeared in that video, the Sotloff family made one simple request of the administration -- and they were rebuffed on that," Barfi told CNN. He declined to elaborate on the request, citing the safety of those who are still being held hostage.

He said the relationship between the Sotloff family and the White House was "very strained."

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"We do not believe they gave us the cooperation (the family needed)," he said.

A senior administration official said U.S. policy is to use "all of our military, intelligence, law enforcement and diplomatic capabilities to bring Americans home safely.

"While we were not able to bring Steven home to his family, that is what we did in his case and what we continue to do in the case of those still being held by (ISIS) and by other groups around the world," the source said.

The official said among its efforts, the administration reached out to more than two dozens countries asking for help "from anyone who may have the influence or information that could assist in securing the release of American citizens behind held hostage in Syria."

But Barfi also criticized the release of information about an unsuccessful U.S. commando raid this summer that attempted to free Foley, Sotloff and others.

"We know that the intelligence community and the White House are enmeshed in a larger game of bureaucratic infighting, and Jim and Steve are pawns in that game. And that's not fair," Barfi said.

"If there continues to be leaks, the Sotloff family will have to speak out to set the record straight."

National Security Council spokeswoman Caitlin Hayden said the administration is still committed to the cases of Sotloff and Foley.

"We understand the very real pain the Sotloff family is feeling at this time. Our thoughts and prayers are with them as they grieve Steven's loss," Hayden said.

"We condemn the murders of Steven and Jim Foley and we remain committed to bringing the perpetrators of these crimes to justice."

Up to $10 million reward

A group of bipartisan senators introduced a bill Monday that would authorize up to $10 million for information leading to the arrest and conviction of anyone involved in the Foley and Sotloff abductions and beheadings.

"James Foley and Steven Sotloff nobly risked their lives in the pursuit of truth, and the United States will not stand idly by after two of its own were brutally murdered at the hands of fundamentally evil and freedom-hating extremists," Sen. Marco Rubio, R-Florida, said in a statement.

Sen. Jeanne Shaheen, D-New Hampshire, echoed that sentiment.

"James and Steven contributed greatly to the world through their reporting, and we must vigorously pursue those responsible for their murders."