WASHINGTON — Did the search for Sgt. Bowe Bergdahl cost the lives of American soldiers?

Since last weekend’s prisoner exchange in which Afghan insurgents turned over Sergeant Bergdahl after five years of captivity, a number of the men who served with him have called him a deserter. Some have gone further, blaming him for the deaths of six to eight soldiers.

That second claim is hardening into a news media narrative. CNN has reported in scrolling headlines that six soldiers died looking for Sergeant Bergdahl after senior American military officials say he wandered off his base. The Daily Beast published an essay by a former member of Sergeant Bergdahl’s battalion, Nathan Bradley Bethea, who linked the search to the deaths of eight soldiers whom he named. “He has finally returned,” Mr. Bethea wrote. “Those men will never have the opportunity.”

But a review of casualty reports and contemporaneous military logs from the Afghanistan war shows that the facts surrounding the eight deaths are far murkier than definitive — even as critics of Sergeant Bergdahl contend that every American combat death in Paktika Province in the months after he disappeared, from July to September 2009, was his fault.

All across Afghanistan, that period was a time of ferocious fighting. President Obama had decided to send a surge of additional troops to improve security, but they had not yet arrived. In Paktika, the eight deaths during that period were up from five in the same three months the previous year. Across Afghanistan, 122 Americans died in that period, up from 58 in 2008.