Update: EA made the news official in a press release just now, confirming a "fall 2013" window for the game's beta.
Battlefield 4 is most certainly a game, as EA confirmed this morning via a trailer for this year's Danger Close shooter, Medal of Honor: Warfighter. According to the publisher, pre-orders of Warfighter's "limited edition" get direct access "to the exclusive Battlefield 4 beta" – of course, we've never actually seen or heard of Battlefield 4 outside of a leaked image revealing its existence a few days ago.
EA's Danger Close studio is responsible for the Medal of Honor series, though Battlefield developer DICE assisted with the first MoH reboot. DICE created the Battlefield series, and it stands to reason that the Swedish studio will also be behind Battlefield 4. We've reached out to EA for more info.
It seems unlikely that this reveal was unintentional, as EA UK marketing man Dan Sheridan tweeted, "Pre-order #MOH Warfighter & get access to #BF4Beta" with a link to the video and preview page. EA's US reps have yet to say a word.
[Thanks to everyone who sent this in!]