This summary is not the rule. The rule text controls.
If someone has liability insurance, that fact usually can't be brought up in court to suggest they were careless or did something wrong. The idea is that just because a person has insurance doesn't mean they were at fault in the situation being argued about. Juries might unfairly assume that having insurance means someone is more likely to blame, so this kind of evidence is normally kept out.
That said, this information can still come up in court for other reasons. For example, it might be used to show that a witness has a reason to be biased, like if they work for the insurance company involved. It can also be used to prove things like who owned a property, who controlled it, or whether someone was acting as an employee or agent for another person or business. In these situations, the insurance information isn't being used to prove fault. It's being used to establish a different fact that matters to the case.
