I don't think we ought to read too much into the licensce photo; I think it was drawn that way simply for comic effect. Within the context of the show, maybe one of the IF's or Madam Foster was with her at the DOT office, made a goofy face at her, she made one back, and naturally that's when the camera went off.
It's fairly common for people to be insecure about their looks, even when they have no need to be. It's endearing, in a way; it's certainly easier to tolerate than an "I'm hot, and I know it" attitude, which is arrogant, annoying, and unattractive, and certainly not the Frankie Foster I know and love.
