The debate over a United States gun trafficking probe known as Operation Fast and Furious is heating up, and the Justice Department is facing questions over its knowledge of the program, which allegedly allowed thousands of guns to “walk” over the border into Mexico. But are they looking in the wrong direction?

In a House Judiciary Committee Hearing on May 3, U.S. Attorney General Eric Holder found himself the target of sharp criticism over the role the Department of Justice and its lead agency on the case, the Bureau of Alchohol, Tobacco and Firearm’s (ATF), played in Fast and Furious.

Most criticism has focused on the operation’s main strategy: allowing suspected “straw buyers” to purchase large quantities of semi-automatic military-style rifles and pistols, in order to track the weapons back to Mexican drug traffickers.

According to a partial transcript of the hearing released by the office of Representative Darrell Issa (R-CA), the congressman accused Holder of trying to cover up his previous knowledge of the program. Issa even insinuated that the Department of Justice bore some responsibility for the death of U.S. Border Patrol agent Brian Terry, who was killed by a Mexican cartel in December. Weapons found at the scene of Terry’s death were traced to Fast and Furious.

When Holder dismissed this allegation as unfounded and offensive, Issa asked: “So what am I going to tell Agent Terry’s mother about how he died at the hand of a gun that was videotaped as it was sold to a straw purchaser fully expecting it to end up in the hands of drug cartels?”

Ever since this controversy first began, Holder has taken care to distance his department from the program, saying it has a strict policy against allowing weapons to cross into Mexico. In a letter sent to Issa and Senator Charles Grassley (R-IA) on May 2, Holder’s office said: “It remains our understanding that ATF’s Operation Fast and Furious did not knowingly permit straw buyers to take guns into Mexico.”

However, interviews with a Phoenix ATF agent who was involved in the operation suggest otherwise. In a recent CBS investigation, agent John Dodson alleges that the “gun walking” strategy was approved by the Department of Justice, and was part of a larger anti-drug effort. The purpose of the operation, Dodson told CBS, was to see where the guns ended up, and use this information to build strong legal cases against Mexican cartels.

Now, a document released by Issa and Grassley’s congressional investigators seems to support this claim. According to a March 10, 2010 memo sent from Assistant Attorney General Lanny Breuer, the Department of Justice approved a wiretap application for suspects targeted in Fast and Furious.

The fact that the ATF was able to get blanket wiretapping approval for the operation undercuts Holder’s claims that his department had no knowledge of its workings. The review process for wiretap applications involves an extensive assessment of the merits of surveillance as well as the initial evidence collected, and must be approved by a judge. Before approving the wiretapping request, Department of Justice officials would have had access to the specific design of the operation, and therefore must have known that it involved allowing individuals to purchase suspicious quantities of arms.

Ultimately, however, the debate misses the real issue. As InSight has previously pointed out, purchasing multiple assault rifles is not, in and of itself, illegal. What’s more, the threshold of evidence needed to prosecute straw buyers is extremely high, which makes cases against these individuals tricky to pursue.

Holder’s (potentially feigned) ignorance is not helping the issue. In order to reshape the debate, he and the Department of Justice need to fully disclose their role in operations like Fast and Furious, offering an informed defense of their purpose: to get to the larger players in the scheme.

Although controversial, such operations are needed both in order to arrest gun-running ringleaders and to help ATF officials understand how weapons are trafficked below the border, none of which can happen if the U.S. authorities limit themselves to arresting suspected straw buyers.