According to the Wikipedia article on Tom Howard (the photographer who famously took a picture of Ruth Snyder's 1928 execution), photographers are banned from U.S. executions (the state of New York unsuccessfully attempted to prosecute Howard and the newspaper he took the photograph on behalf of); why is this so?
Existing case law on this issue is readily available via Lawson v Dixon in North Carolina and Garrett v Estelle in Texas. In this case, and in most states, the legal authority lies with the Warden to maintain "the supervision and control" of the prison.
"...plaintiffs David Lawson, Phillip J. Donahue, and James Arnold do not have a right under either the First or Fourteenth Amendments to the United States Constitution or under Article 1, Section 14 of the North Carolina Constitution to audiotape or videotape plaintiff Lawson's scheduled execution, see Houchins v. KQED, Inc., 438 U.S. 1, 57 L.Ed.2d 553 (1978); Pell v. Procunier, 417 U.S. 817, 41 L.Ed.2d 495 (1974); Saxbe v. Washington Post Co., 417 U.S. 843, 41 L.Ed.2d 514 (1974); Garrett v. Estelle, 556 F.2d 1274 (5th Cir. 1977); that under N.C.G.S. 15-190 the execution is under the supervision and control of Warden Dixon; and that, as a matter of law, neither Secretary Freeman nor Warden Dixon can be mandamused to permit the requested audiotaping or videotaping;"
As the quote above states, also explore the cited case law: