Another question since I stayed clear of insurances so far: What happens if I actually loose something and the company has to replace it? Do say "No problem, no need for proof it was really stolen or it's a fraud attempt, here's your (insert value here) and have fun with it"? Does the insurance rate rise afterwards or (when) do they cancel the contract? Sorry if this sounds silly or naive, but I really have no experience with insurances at all.
My insurance company (home insurance as I'm not a pro) told me that if I'm in the USA or Canada, they'd like a police report stating the loss, but if I'm in Mexico, or a country that the police will hassle me in, they'd rather I not take the risk of reporting it.
My home insurance also didn't require an itemized list, just the ability to prove what I had in the event of loss. So I keep a copy of the receipts for all my gear in a folder in a safe, and a PDF copy of all receipts on my laptop, and in the cloud with DropBox.
I believe this is partially because my insurance plan also covers "mysterious disappearance" without exclusion.