What I was astonished to find out is that insurers actually have people or departments whose sole job is to find reasons not to pay and how they cling to absolutely every detail, true or not.

More or less the same thing happened to me with a 6 months travel insurance. I had an unfortunate series of light medical problems that racked up about 1500 EUR. I was somehow lucky that I over-informed the insurer anytime anything concerned them and they pre-approved each doctor's visit. When it was time to get my money back, they denied the claim saying that I flew back home one month into the trip (and then left again) and that legally concluded my trip. That was, of course, non sense.

I wrote them a letter saying that if they don't return my money in 30 days, I will fill in a complaint with the insurance oversight authority in my country. They didn't so I did. The nice part is that this authority shoots first and asks questions later so in a few days I got a really passive aggressive letter saying they will be paying in full, that they already decided that a week before so there was no need for me to file the complaint (I was, of course, not informed) and they asked me to withdraw my complaint.