I worked in the industry yes, I am an accountant and was working as a specialised systems accountant hence why i was working with MI people etc
Whilst I have already explained to you why your wrong keep jumping up and down about something that to the vast majority of people is nothing but terminology. I could do just the same with the people who mix up profit and loss and balance sheet for example.
But I will repeat for you, not that I expect you will take any notice.
They spend a vast amount analysing (note I haven't mentioned probability or stats here) looking for past trends to be able to use them for commercial advantage.
One commercial advantage, in fact the main one, is to be able to correctly split the risks and therefore offer premiums based on the best model possible for predicting the risk of that insured. One of the commonly accepted risk factors identified is that people who have had non-fault claims show a history of being more likely to have another than those who have not. Its simple facts pulled from massive amounts of data that the actuaries would generate. The colour of a car also was detectable, as were plenty of other factors people easily accept like, age, driving experience etc
But then after very detailed analysis gets done the marketing people get to manipulate the target offerings.
Just taking two examples at a high level I remember from years ago.
Married men 35-45 with kids and a wife, typical mondeo driver at the time, was loss making business due to the market believing they were low risk drivers. Plenty of these about so a hard segment to ignore when needing a decent level of policies written to support the overheads.
25-35 year old single males with high performance cars were the top earning policies for the ins cos.
General population would not accept that "mondeo man" would cost on average more than "boy racer" and hence the premiums that could be charged were out of line with actual data.
So insurance is not based on nonsense, its based on lots of data with a hint of marketing. Its a highly competitive industry (arguably wasn't so much until direct line stirred it up). Any of the companies would take any opportunity to grab profitable business from the others when possible, so truly understanding the claims data was business critical.
Plenty of years insurance companies would only make money from the investments income whilst they had the premiums available before they needed to pay them out as claims. Its one of the reasons there is strict liquidity rules in place so they can't invest everything and not have the funds available to deal with claims.
You do make me laugh though expecting anyone who works in insurance to be an expert in stats, probability etc
The reality is that only a few people do, they are highly trained and have access to commercially sensitive material. The facts that I worked with these people directly was why I got involved and picked up bits of knowledge, I spent a lot of my time working under NDAs (non disclosure agreements) due to the sensitivity of the data I could have access to.
If you want to know who actually understands the stats/data/probabilities etc this will give you a good summary of the people who are inside ins cos working on this data
https://www.prospects.ac.uk/job-profiles/actuary