The question is akin to this,
If you walked into a crowded parking deck and hit the unlock button on your key fob for your Honda Accord and the nearby Maserati lit up, the door swung open and a voice came over the parking deck speakers and said your name and welcomed you into the vehicle as if it were your own then when you sat down in the car the key also just happened to fit and start the engine... then would you take the car?
The voice over the speaker system is giving the man the car, even if the voice is lying he might think its a publicity stunt and play along.
The OP's Bitcoin example involves the theft of Bitcoin without almost any repercussions. The question here boils down to an ethical one, without the chance of being caught do you steal a random's Bitcoins.
Many will steal them, and most of the people that will steal them have to rationalize the theft to themselves. ("No one should put so many coins in one address!", "God gave them to me", "Fate, nuff said", etc..)
However no rationalization is needed in your example because you are literally being given a car and the whole thing smells of a publicity stunt. In fact he probably expects himself to be apart of a show on TV and is probably researching hidden camera shows to see if any filmed in the local area.
I am tired and rambling, if I make no sense please disregard the above.