Yes, you're paranoid...
But imagine a terorrist, lets call him Osama Been Late or something, sends a 'new' video of himself to a local newsstation, threatening to pollute the World's stores of Jarlsberg cheese with cheag Edam from the USA?
With the ENF tampered with the Keystone Cops can say that 'hey, this is an edited video, the guy behind the threats haven't made a reliable appearance in yoinks, and is probably dead'
In fact, it's in the terrorists own interest to keep the ENF as some sort of 'Open Source Digital Fingerprint' to prove that they are alive, well, and hoping that everyone else isn't.
(And if the ENF signature matched Acapulco, Las Vegas or another nice vacation location... they're obviously very well... )