One thing you need to examine in comparing policies is whether the insurance company is the primary or secondary payer. If they are the secondary, they will not pay anything until whatever other coverage you have kicks in. That is not for me, and I always choose a policy where they are the PRIMARY payer for lost baggage, theft, etc.
I did collect for theft in Tahiti. We were waiting at a hotel for transit to the airport, and my daughter's carryon was rifled and some items stolen. We were reimbursed with some depreciation taken. Still, it was something.
I have also collected from my health insurance company here for medical expenses overseas. I collected for seeing a doctor in Canada, Italy, and Jamaica - you just need to have the letter from the doctor explaining what was done and why.
BTW, on my last cruise I asked for some cold medication from the ship's doctor. I was told that unless I scheduled and paid for a visit to the doctor - at $65 - he could not give me anything, even over-the-counter medication. I found some Dristan at the next port.