For UF, it really depends on the size of the battle that you're talking about, and the willingness of the participants to keep it a secret - like, no matter how much they want to fight each other, they know making it overly public won't do anyone any favours.
Like, in my 'verse, you've got the...basically the equivalent of the MiB that does a lot of ass-covering for stuff like this. Fine, they may be involved in a lot of it, but they always have a cover story involved, and several decent PR departments working on a variety of explanation scenarios at all times, so that it doesn't always come down to "gas leak" or "military training accident".
They even basically have an OSHI- backup plan when they know a few press releases/talking to the right reporters won't work, and that's a TV show called "Surprise Fiction" which is basically a reality show/candid-camera hybrid, portraying really weird/random things (which people may perceive to be fantastical events), then explaining the mechanics behind them (sort-of Mythbusters style). They do a big, like 2-hour special when something goes really, really wrong, but do enough regular episodes (generally stuff they've just made up themselves) so that it doesn't feel like a cover-up mechanic.
This all works because all parties involved - the Agency themselves, the Faerie courts and assorted smaller factions, despite their allegiances or general opinion about each other, know that getting this stuff out there, and into the public eye would do no good for anyone, and only make all of their lives harder.
So, basically, if you can get the people involved in your battle to acknowledge this - and have it so no-one is stupid enough to live-stream the carnage to the internet, call the press, or throw a goblin (or whatever you're dealing with) corpses into the town square, there would be ways that you could get around needing to make it full fantasy.