The reality is that a certification on its own really means the participant has completed a minimum set of requirements to achieve a pass and get a card allowing them to go forth and gain experience. Properly documenting your dives and being able to show it is more important IMO to determine your qualifications than the certification card in your wallet.
The insurance company may not see it the same way as they see the certification card a documentation of ability (a clearly defined set of minimum requirements) going beyond what you are certified to do is likely deemed exceeding your qualifications. In my opinion certification and experience are both required to determine what a diver is qualified to do. but that is only my opinion.
As you said, both experience and certification are necessary. If a diver only has experience it will lack the formal training. There is no guarantee of being doing the right things on the deeper dives and can be an accident waiting to happen. Extreme case, but you've probably heard of the father and son who had been gradually building up to cave dive and had done several cave dives. Experience? No, they died. It's very hard to judge things on an individual basis and an insurance policy has to be clear and applied to everyone in general without room for subjectivity or interpretations.