Deziel, 51, was arrested Thursday after she took a loaded handgun in a carry-on bag through airport security and onto the plane.
TMZ said she told police she forgot she had the gun in her bag.
She explained she bought the Smith & Wesson 38 special revolver because of death threats she had been receiving, but did not offer details about who had been threatening her or why.
Deziel also said she had a concealed handgun license in Texas, TMZ reported.
Deziel married Nugent in 1989 and they have one child together. Nugent, 64, is a rocker, TV and radio personality and National Rifle Association board member.