You're right,

He isn't directly stealing from his bandmates because he isn't making physical copies of the sheet music covered under for PA.

But his deal with Warner likely includes a revenue share. CDs are considered royalty bearing objects, if Lars wants a copy of his own CD, he has to purchase it from his publisher, he can't just have one. The publisher and performer negotiate rates and they're surprisingly high, even though they consider it a wholesale price. The publisher then splits the revenue according to their negotiated deal with the band.

There are several layers of copyright, I will ignore fair use, since proponents of DRM ignore fair use. SR is the Sound Recording copyright, it is almost always held by the Record Company, in this case Warner. Warner is known for little flexibility with artists so I would assume they hold the SR. SR basically covers the recording. If they were to issue a remix, it would have a new SR. If I recorded one of their songs, I could get a new SR in my name. PA is the Performing Arts copyright, and is held by the authors of the song, it covers the underlying structure, lyrics and notes. This is held by (Hetfield / Ulrich / Hammett / Trujillo) according to the album notes. This means that Ulrich stole from Warner and his three bandmates. He's not the only holder of copyright for that music.