I think the mark as stolen feature would be a reasonable one. It could tell the person adding it that the camera was stolen, like if they purchased it online from the person who stole it (I mean, how many home robbers have a Blink system themselves to add a stolen camera to?).
And maybe Blink could identify the IP address of someone that’s trying to add the stolen camera to another sync module.
But without a subpoena or warrant, the ISP of the person who’s trying to add the stolen camera would never give out any personally identifiable information to allow that individual to be identified.
And sorry, but forget about having the camera arm and record remotely to “catch” the person that’s trying to add the stolen camera. That would open such a gigantic privacy can of worms that Blink wouldn’t want to touch with a 10 foot pole.