That is incorrect, you can prove that you are the owner of the private key that spent the bitcoins if you wish. Anyway this seems like a silly argument, with physical cash how can you prove that you paid X with that cash like in the scenario you outline?
My point is that as payments become more and more digital then we must be wary of what that means in terms of data mining and things like that.
Now you've reassociated yourself with your Bitcoin account.
When you report a cash theft, the police don't go looking for the serial numbers of the notes (usually). They look for other evidence, like your house being broken into and the burglar leaving evidence behind. Imagine you've created a situation where there is no evidence that you live in your own house!
You can prove you were the owner of the spent coins to the police if you wish but this doesn't allow the data mining company to know all of your financial history.
My point is that as payments become more and more digital then we must be wary of what that means in terms of data mining and things like that.