"It suggests to me that, on the million-to-one, once-in-a-lifetime scenario that something did indeed go wrong, and that someone was indeed seriously injured, the venue would be doing their damnedest to make sure it was the promoter's insurance that paid for it, not theirs."

Of course they would - and similarly, the promoter would try to push the liability onto the venue. The important part of that statement is that it is the promoter's insurance which would pick up the tab, rather than the promoter himself - who probably doesn't have the money.