That's just cheating. They're comparing people who have been unemployed long enough to lose the benefits to the recently unemployed. Obviously the former group will have underrepresented the people most independently inclined to look for a job, because more of those people will have found one before becoming members of that group.

You have to qualify for the expanded unemployment benefits but I suppose that's a detail to be overlooked if it's inconvenient.

"You have to qualify for the expanded unemployment benefits" is exactly the point. The criteria for qualification causes a disparity between the experimental group and the control group, which invalidates the experiment.