Ok Fluffy, not sure where you are getting your information from but I believe I'm pretty well qualified to correct a few of your assumptions.
Firstly, ANY dog can be aggressive. Every living creature has a limit as to how much of what it doesn't like that it will tolerate. Especially when in pain and a first look of the source of pain before pain relief is administered.
I myself have been on the receiving end of pain related aggression from animals some I know on a personal level that have played with my child on floor with them the previous week. I haven't blamed any of them as it was in a vet exam situation, it's highly stressful and being poked and prodded in a painful area will cause them to startle.
You mentioned that she was fine post spay, she had painkillers and they are generally very tender after spay, not excruciating pain.
Also on your second post you did mention that your dog has got out a couple of times and even though you live in a quiet area the only real risk would be for an RTA to happen albeit unlikely.
It's not just RTA that you need 3rd party cover for but thankfully you are looking into it. And neither is it about the dent YOUR dog makes if the car hits the dog.
Some of accidents have been caused because road users have swerved to not hit a dog and have hit a tree/lamp post/another car/pedestrian etc. The dog can come away unscathed but has left a path of destruction in its wake. You would need insurance for that.
However, 1 million isn't a lot when it comes to litigation. Have a look online at some cases.
I suppose I'm a bit confused as to why it's such an issue not getting an insurance policy if money isn't an issue? Also there are so many knowledgable people on this thread, plus the majority of posters are giving their reasons as to why it's beneficial. I fear you will make your decision rather ill informed of all the facts and the different issues that can arise from not having insurance.
As you can tell in a huge advocate for pet insurance, but only because I'm so informed of all the alternatives, regardless of personal wealth. I'm only badgering because I'd hate for you or pet to get caught out because you have been given the full picture.