Johnson filed the lawsuit in April on behalf of the reporter, identified only as Jane Doe.
An attorney for Splash News & Picture Agency, the paparazzi firm that surreptitiously shot Ledger in the freelancer's hotel room in 2006, said Tuesday he could not comment.
The video surfaced after Ledger's death last January. "Entertainment Tonight" had plans to air part of the footage and showed a teaser, but backed off after receiving pressure from stars and publicists. The full video eventually surfaced on the Internet, but became increasingly difficult to find over time. On it, Ledger is heard talking about his wife and daughter and prior drug use.
Splash had contended throughout the case that the reporter did not have a valid claim since her face in the tape was blurred. They argued that only Ledger could claim wrongdoing, and his privacy rights died with him. A judge initially agreed with the argument, but later restored many of the suit's allegations.
A judge recently rejected motions by Johnson to inspect Splash's computer and e-mail records and take the deposition of the shooter, who now lives in Japan.
Johnson had sought to question the man about who paid for the drugs that appeared in the video. The reporter's lawsuit contended that Splash's employees provided the drugs to Ledger.
Another case seeking the release of Ledger's $10 million life insurance payout to his daughter, Matilda Rose, is currently scheduled for an August trial in Los Angeles Superior Court.