Hmm.. Bitcoin insurance? Sound great but.. Well.. like you say, how can we make sure the person is not cheating? I mean.. Bitcoin was created with anonymous and privacy in mind. So, it is hard to track whether the 'robber' is the person him/her self.
However, if we have a trade insurance.. it will be better.
Insurance companies can employ crypto currency specialists to protect their interest, and I have dealt with those specialist earlier when my house was broken into last year.
They will find "small" things not to pay claims ....like :
1. Sorry sir, you anti-virus was not updated at the time....
2. Sorry madam, you should have implemented 2FA on your online wallet....
3. Sorry sir, your webcam was not covered....
They always find ingenius reasons not to pay.... and it's always your fualt. {I once had a claim for damage to my car in a 4 car pile up... I was in the middle... and they denied my claim, because according to them,
one of the 4 tyres on my car was too smooth, and not within road traffic regulations.
They will jump on the opportunity.... Bitcoins have many loopholes for them not to pay.