In the criminal sense, you're correct.

In the civil law sense, you'd be wrong. Using a camera to record a performance is an act of copying and is subject to copyright law. Generally, if the performers and/or the owner of the copyright don't give you permission to record the show, you don't have the right to do so. (Note that taking pictures or recording short clips is usually but not always regarded as fair use. Recording an entire performance without permission is rarely treated as fair use.)

However, recording the performance is also an act of creation, resulting in a derivative work that has its own copyright, but one which is useless without a copyright license to the underlying performance.