This summary is not the rule. The rule text controls.
If someone has liability insurance, that fact usually can't be used in court to show they were careless or did something wrong. Juries might assume that a person with insurance is more likely to be at fault, or might go easier on someone without insurance, so the law keeps this information out of the case in most situations.
There are exceptions, though. A judge can allow evidence of insurance if it's being used for a different reason, not to prove fault. For example, it might come up to show that a witness is biased because they work for the insurance company. It can also be used to prove who owns or controls property, or who has authority over something involved in the case.
The main point is that insurance status stays out of the conversation when it comes to deciding who acted wrongly. It can only be brought in when it serves some other legitimate purpose in the case.
