Here a few sequences from our absolute zero budget action short Nat, followed by some making-of:https://www.youtube.com/watch?v=RvIFd6xnEnA&feature=youtu.be&t=22s
No rigs, no stunt team, no DP, no microphones other than embedded to the cameras, and no transport: walked to the public locations - with some snacks in a bag. Just 2 friends with - different - cameras, and a (non-actor) co-fighter.
The shoot was done in half the time I thought it would. Some shots for this short I had to edit in from the rehearsal just before the actual shoot for the action to make sense, but they are by definition slow. Therefore next time I'd rehearse before the day on location with the cameras because: the location and the camera are actors in fight scenes more than in non-fight scenes; and precision of the movements as seen on camera must be thoroughly prepared. Hopefully with equipment and budget for everyone and for insurance.
@Joe Piechura: Yes!
You really want to read the small print.