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 argue whether they acted carelessly or did something wrong. For example, a lawyer can't tell the jury "the defendant had insurance, so they must have been careless" or "they didn't have insurance, so they must have been careful." Insurance coverage just doesn't prove fault one way or the other, so it stays out of that part of the case.
However, this information can still come up for other reasons. If insurance evidence helps prove something else, like who owned a piece of property, who was in control of a situation, who was working for whom, or whether a witness is biased, then it can be allowed. The key question is why the evidence is being used. If it's about proving fault, insurance stays out. If it's about proving something else entirely, it may be allowed in.