Interestingly, Razor1911, a team that frequently cracks games for pirating, has just released a modified .exe that lets you bypass Origin completely (AKA - Origin doesn't have to be installed). It seems Razor aren't very trusting of Origin/EA, not difficult to understand. Sadly, looking at a majority of posts on Reddit it seems people openly and explicitly trust Razor1911, a pirating team, more than EA, which really says a lot.

There's two issues with this as far as I see: 1) Could be unsafe (time will tell for this). 2) EA could easily patch the game to detect this and stop it. Further, it would not be a stretch for EA AT ALL to start banning people who do this. There's some discussion going on whether banning players for this would be legal. Someone without Origin has not necessarily accepted Origin's EULA in the first place. The answer lies in the BF3 EULA, for anyone dedicated enough to dig through it. Now I'm actually happy that I don't get BF3 for another ~9 days, with any luck some of the dust will settle by the time I get my grubby hands on it.

To my understanding, this is a crack for LEGAL copies only, intended solely for people who legitimately bought BF3 but hate Origin .I won't link to it directly because it might be against some forum rule, and I can't guarantee it's safe.