Presumably not, because "the key is broken" is not the same as "I refuse to hand over the keys". This law, rightly or wrongly, is concerned with the latter concept.
I guess "Ah crap, it was on my keys earlier, I must have lost it - I can't do anything" would be a grey area!
If you were prepared to lose your device, it would be easier to ditch it than ditch the keys but, again, not all criminals think that far ahead. I read that they caught Dread Pirate Roberts because he thought he would never get caught (in a public library!)
Also, if you have a backup key somewhere, you haven't lost any data or your machine.