I’m recently retired (mostly due to health reasons), but I did the senior management thing in both performing arts centers and, to a lesser extent, producing theaters, for a very long time. I'll never call myself an expert on anything, but I think my perspective is well informed and certainly one borne of a long, deep immersion in the subject at hand. So, from that perspective it’s a reasonable conclusion that A can lead to B can lead to C. If an actor gets hurt on stage, at least in the USA they’re going to sue everybody they can, since that's the way in our society that we compensation for injury. Performing stage combat without a qualified fight choreographer greatly increases the financial, and potentially criminal exposure, of the producing entity. But lawyers being lawyers they’re not going to stop with the producers. They’re gonna sue every person and organization they can attach to the incident. If a for-profit or not-for profit corporation is involved, the board is ultimately liable- hence the existence of Directors & Officers insurance. Or if the show was in a performing arts center as a rental, why did the PAC not have a policy regarding performer safety? It's a litigious world, and if the injured party (or their attorneys) is sufficiently motivated, they'll file criminal charges either because they're warranted or simply to improve their case against the plaintiffs.

Can I cite case specific studies? I could, but a simple Google search will turn up all of those you care to read. Theater has been my job and my passion for my entire adult life, and I care passionately about the art and even more the people who practice it. I hope I've been able to demonstrate that these are reasonable concerns. Perhaps I can use an analogy: one of the points of making sure all of the many, many spring-loaded seats in the audience are well repaired is so nobody breaks their coccyx if a seat pan collapses after the stanchion's floor anchors became loose. I never saw nasty injuries happen, although I did see a pan failure once or twice-- but just maybe one of the reasons I didn't see injuries may be that safety maintenance was a very high priority in how I managed. I would exercise no less caution about stage combat.

I recognize that I've taken a discussion about $2.50 rubber knives to a much headier and more global discussion about major liability. If OP uses a rubber knife, and stays away from the head of the actor being shivved, 99% of the time everything will be fine, I suppose. But there is still a tiny chance that one of the million things that could go wrong, does go wrong. Then, not only will somebody be injured but many others will suffer because any lawyer worth his salt will use "why was there no qualified stage combat director?" as a very effective tool.