By CNN's Charley Keyes

The Marine Corps is fighting back against a newspaper report that it exaggerated the bravery of a hero of the Afghanistan war who received the nation's highest military honor.

President Barack Obama awarded Cpl. Dakota Meyer the Medal of Honor at a White House ceremony in September and spoke about Meyer's heroism in trying to rescue fallen comrades, returning again and again to the middle of an ambush to aid both Americans and Afghan troops.

McClatchy Newspapers, which conducted an investigation into the accounts, said on its website that parts of the Marine Corps' account of the battle were "untrue, unsubstantiated or exaggerated." The article noted the exaggerations probably were unnecessary and that Meyer did deserve the medal for his heroic acts.

In a statement Wednesday, the Marine Corps said it firmly stands behind "the Medal of Honor (MOH) process and the conclusion that this Marine rightly deserved the nation's highest military honor."

The Marines say the award is "entirely appropriate and well-deserved," and that their investigation as part of the award process focused on direct eyewitness accounts and other recorded information.

But the Marines do admit that over the course of a six-hour battle, not every witness had "equal and accurate visibility or situational clarity on every activity."

One issue of contention is a description, a "narrative," of that day posted online by the Marines, which included information from Meyer himself that was separate from the formal investigation that led to the award.

"Sworn statements by Meyer and others who participated in the battle indicate that he didn't save the lives of 13 U.S. service members, leave his vehicle to scoop up 24 Afghans on his first two rescue runs or lead the final push to retrieve the four dead Americans," according to the McClatchy report.

"The statements also offer no proof that the 23-year-old Kentucky native 'personally killed at least eight Taliban insurgents,' as the account on the Marine Corps website says. The driver of Meyer's vehicle attested to seeing 'a single enemy go down.'"

The Marine Corps said Meyer's narrative "was posted on the Headquarters Marine Corps webpage to allow the American public to read Cpl. Meyer's personal account of the sequence of events and actions on this day."

"We supported this communication method in large part because of Sgt. Meyer's personal desire to not retell with each interview, and thereby re-live, what he calls the 'worst day of his life."

Meyer was a corporal in the Marine Corps when he served in Afghanistan and is now a sergeant.

That "Heroic Action" summary entry, as the newspaper group pointed out, now states that it "was compiled in collaboration with Sgt. Dakota Meyer's personal account and HQMC (Headquarters Marine Corps) Division of Public Affairs.

Meyer, contacted by CNN via e-mail, had no comment.

In the White House ceremony, Obama praised Meyer as "an American who placed himself in the thick of the fight - again and again and again."

"The story of what Dakota did next will be told for generations," the president said, describing how Meyer kept returning to the fight.

"For a fourth time, they went back. Dakota was now wounded in the arm. Their vehicle was riddled with bullets and shrapnel," Obama said. "Dakota later confessed, 'I didn't think I was going to die. I knew I was.' But still they pushed on, finding the wounded, delivering them to safety."

"And then, for a fifth time, they went back - into the fury of that village, under fire that seemed to come from every window, every doorway, every alley. And when they finally got to those trapped Americans, Dakota jumped out. And he ran toward them. Drawing all those enemy guns on himself, bullets kicking up the dirt all around him. He kept going until he came upon those four Americans, laying where they fell, together as one team," Obama continued.

"Dakota and the others who had joined him knelt down, picked up their comrades and - through all those bullets, all the smoke, all the chaos - carried them out, one by one. Because, as Dakota says, 'That's what you do for a brother,'" the president said, with Meyer at his side.

The president's comments that day were based on "the extensive documentation provided by the Department of Defense and the Marine Corps, including sworn testimony from Sgt. Meyer himself and sworn eyewitness testimonies of others present at the scene," White House press secretary Jay Carney told reporters Thursday.

The Marine Corps says the official citation, the heart of the formal investigation, was true.

"We are personally very disappointed in the McClatchy Newspapers' decision to publish the article, "Marines Promoted Inflated Story for Medal of Honor Winner" alleging that the Marine Corps embellished Corporal Dakota Meyer's story," the Marine Corps statement says. "The accomplishments described in the MOH citation are valid, supported by two eyewitnesses as required, and confirm the merits of the MOH properly awarded to Cpl. Meyer."

Sen. Jim Webb, D-Virginia, a Marine combat veteran in Vietnam, gave his support to the Marine Corps and Meyer.

"Given the Marine Corps' long tradition of rigid standards and its thorough review process regarding recommendations for combat awards, I have no doubt that Sergeant Meyer has been appropriately recognized for his actions on September 8, 2009, in Afghanistan," Webb said in a statement issued by his office. "Out of respect for the obvious heroism of Sergeant Meyer, it is important that any discussion of this matter begin with this recognition."