exactly. Your physical fingerprint is different, under the law, than something you keep inside your head. They can't compel you to reveal something you keep inside your head, but they can compel you to place your physical finger on the button.
The answer is, if you find yourself in a situation like this, simply power down the phone. That's it. On power-up the phone will require the PIN, and that's that.
This is why cops in the UK are "mugging" suspects while they're using their phones. Armed with a warrant, they will come at all angles in force and in complete surprise, giving the suspect zero chance of powering down his phone. They're even going so far as to assign cops to stay with the phone 24/7, preventing it from locking, while they get the info they need from it.
So if you're worried about your fingerprint, don't be. Your fingerprint has nothing to do with what cops will do to try to get your information.
I think it's time for a remote service that periodically--every half hour, every five minutes, whatever--locks your phone no matter what you're doing on it, and requires a PIN to unlock. But even then, the cops would simply go into a Faraday cage. That means the system must be on your phone itself, then, and not require a remote trigger. Maybe the unlock can be remotely validated. Maybe lack of remote validation after three locks ends up wiping your phone. But then the cops just go to Google or Apple and demand to see the backup they're storing.
And on, and on.