There's a little bit of a difference between breaking a window (noise, glass everywhere), and discretely walking in through your front door and out with your jewellery.
I don't understand the qualifier "in that situation": the user cannot determine what the "situation" may be at some point in the future.
I do use the fingerprint reader on my iPhone, and I believe that the fingerprint data is never sent to another device. Ever.
There are real problems to using the iPhone fingerprint with apps, in that the apps tells me it needs to store an encrypted version of my password on iCloud in order to enable fingerprint unlock. The Bad Guys could get my encrypted password and I might never know.
But I wouldn't have to change my fingerprint in that case.
Or think about locking your phone. Most people only want to stop their friends and family - they're not going to copy you fingerprint. Even FBI nearly defeated by TouchID. (You're probably thinking that they could have easily bypassed it, but they only had 48 hours to do so.)