No she doesn't. as you note, her bosses can pull whatever they want - - she's their employee and doesn't have any "right" to have ANYTHING published, let alone a small, mean-spirited snipe at some old personal foe, which ends up marring what was supposed to be a homage to Reagan.
And they can publish anything they want, including a personal snipe by one of their writers.
It may not be obvious to you, but the WSJ wants to slam this guy just as hard as Peggy does. Otherwise, they would not have published it.