Further to Mike's citation, here's the decision (
Dowling v. United States, 473 U.S. 207 (1985)) in the Dowling case; it was a 6-3 decision, so clearly there's no unanimity on this issue.
Most importantly, the court held that "the statutorily defined property rights of a copyright holder have a character distinct from the possessory interest of the owner of simple 'goods, wares, [or] merchandise,' interference with copyright does not easily equate with theft, conversion, or fraud."
This decision represents case law, which would protect you against allegations of theft in a music-copying case. But while their marketing campaign may call it theft, they're not alleging theft in their lawsuits—and this decision offers no protection for copyright infringement.