Ethically, this is really simple, whether your the OP or the guy with the bike in the apartment basement. If it's not your bike it's not OK to just take it. There is absolutely no gray area here.

Now practically, I agree that providing loving homes for abandoned bikes is a wonderful thing. You still have to go through the current owner to become the new owner. In some extreme cases the "current owner" may have become the owner of the property in which the bike has been abandoned.

Clue to Chop61 (who I hope is at least somewhat joking): if you feel the need to repaint a bike you "claim", you're probably stealing.