It’s hard to understand why the FBI would want to expose itself to ridicule in this way.
I can see why the FBI and any other agency would want to prevent abuse of its symbols, and I agree with @laureth that the right to use them as badges of authority does not belong to everyone. A lot of things have become easier to reproduce fraudulently and misuse now that we have the Internet and high-powered graphics programs to facilitate it. This is a much bigger issue than the FBI’s authority, and no one knows what to do about the larger issue yet. Giving information about something is hardly the same thing as trying to pass yourself off as a legitimate wielder of the authority it represents.
But there’s also the point that authority vested in a badge depends on its recognizability.
More important still, to me, is the idea that the government would try to impose control over how the people write about its functions and branches. If this prohibition is upheld, how long before it becomes illegal to draw a cartoon image of the president?