That is mostly true, according to a 4 October 2011 Reuters article Secret panel can put Americans on "kill list':
American militants like Anwar al-Awlaki are placed on a kill or capture list by a secretive panel of senior government officials, which then informs the president of its decisions, according to officials.
There is no public record of the operations or decisions of the panel, which is a subset of the White House's National Security Council, several current and former officials said. Neither is there any law establishing its existence or setting out the rules by which it is supposed to operate.
The panel was behind the decision to add Awlaki, a U.S.-born militant preacher with alleged al Qaeda connections, to the target list. He was killed by a CIA drone strike in Yemen late last month.
The role of the president in ordering or ratifying a decision to target a citizen is fuzzy. White House spokesman Tommy Vietor declined to discuss anything about the process.
Current and former officials said that to the best of their knowledge, Awlaki, who the White House said was a key figure in al Qaeda in the Arabian Peninsula, al Qaeda's Yemen-based affiliate, had been the only American put on a government list targeting people for capture or death due to their alleged involvement with militants.
The White House is portraying the killing of Awlaki as a demonstration of President Barack Obama's toughness toward militants who threaten the United States. But the process that led to Awlaki's killing has drawn fierce criticism from both the political left and right.
In an ironic turn, Obama, who ran for president denouncing predecessor George W. Bush's expansive use of executive power in his "war on terrorism," is being attacked in some quarters for using similar tactics. They include secret legal justifications and undisclosed intelligence assessments.
Liberals criticized the drone attack on an American citizen as extra-judicial murder.
Conservatives criticized Obama for refusing to release a Justice Department legal opinion that reportedly justified killing Awlaki. They accuse Obama of hypocrisy, noting his administration insisted on publishing Bush-era administration legal memos justifying the use of interrogation techniques many equate with torture, but refused to make public its rationale for killing a citizen without due process.
Some details about how the administration went about targeting Awlaki emerged on Tuesday when the top Democrat on the House Intelligence Committee, Representative Dutch Ruppersberger, was asked by reporters about the killing.
The process involves "going through the National Security Council, then it eventually goes to the president, but the National Security Council does the investigation, they have lawyers, they review, they look at the situation, you have input from the military, and also, we make sure that we follow international law," Ruppersberger said.
They said targeting recommendations are drawn up by a committee of mid-level National Security Council and agency officials. Their recommendations are then sent to the panel of NSC "principals," meaning Cabinet secretaries and intelligence unit chiefs, for approval. The panel of principals could have different memberships when considering different operational issues, they said.
See also the September 2016 article When The U.S. Military Strikes, White House Points To A 2001 Measure which explains that the language:
That the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons
is interpreted very broadly by the president:
Today, a decade and a half later, the Obama administration argues that the authorization continues to apply to U.S. military actions in Afghanistan. Also, that it applies in Iraq, in Syria, and beyond — including the ongoing air campaign in Libya, against ISIS — a group that did not exist 15 years ago.
See also A New Authorization for Use of Military Force Against the Islamic State: Issues and Current Proposals which says:
The President in his August 2014 notifications to Congress of deployments and airstrikes in Iraq indicated his powers as Commander in Chief and Chief Executive under Article II of the Constitution gave him authority to undertake such action. Obama Administration officials and the President’s September 2014 notifications4 to Congress for airstrikes and other actions in Iraq and Syria, however, stated that two enacted authorizations for use of military force (AUMFs), the Authorization for Use of Military Force (2001 AUMF; P.L. 107-40), and the Authorization for Use of Military Force Against Iraq Resolution of 2002 (2002 AUMF; P.L. 107-243), provide authorization for certain U.S. military strikes against the Islamic State in Iraq and Syria, as well as the Khorasan Group of Al Qaeda in Syria.