A dog that is only half trusted. When it was common for people to put biscuits and pies on the windowsill to cool, a savvy dog might snatch them. A dog that, while polite enough while there's people in the room, will certainly stick his nose in the dip if there's no one in the room. Can also apply to two-faced, sneaky people.
Keep an eye on my plate while I wash up, that dog's a biscuit eater.