Hi, Steve in Kent,
I do not know about your country, but I think (Mark, mds uke or Jay, blueuke, might chime in) in the USA the venue typically has insurance. Of course, anyone can be sued.
An example that I know from first-hand experience (as an expert testimony): in a small Illinois town, four years ago, at a high school baseball game, a car was backing up in the school parking lot and the driver hit, at slow speed, a wooden telephone pole. It came down and, regrettably, a child and mother were underneath it; the child survived with spinal damage and surgery (but still ambulatory), and his mother died from being crushed.
I know that the injured parties sued the school (for not blocking the pole in the parking lot with barriers), the telephone company (for not having the pole secured), and the driver (for nudging the pole; apparently, the car had little damage). It was a huge case and a big settlement.
So, perhaps the venue will be less liable if everyone (even the uke group) has insurance? Some say that attorneys will target the limits of insurance liability, particularly for those without personal "deep pockets", so having all parties insured will "spread the risk". I could be wrong on this, though.
Honestly, with today's litigious society, I would not want to host people at any event (this is personally my mantra, not those of others). Recently, at a US college, there was a lawsuit over a fraternity hazing incident. We know one of the families involved. The victim--and he was a victim, no question there-- sued the college, the national fraternity, and personally sued the fraternity leaders, such as the President, VP, etc. (these are 18-year old dependent kids, so, in essence, their families were sued). Oh my! Long tentacles!
My wife was the president of her high school class and previously helped arrange class reunions; once we found out that organizers of such events can be sued, personally (e.g. drunk driving incident by a patron, falling telephone poles, etc.), she stepped down as president and organizer--in writing (paper trail).
Sad. I think in your country, if one sues and loses, the losing party pays for the litigation expenses of the acquitted, no? Sort of a checks-and-balances, right? I may be wrong. Here, it's a frigging wild, wild west free-for-all, with lottery mentality.