The dogs aren't purposefully trained to give false positives, that's just a side effect of how social dogs are. They want to please their handler and the handler gives them rewards.
It would be damn hard to prove the last, but what is relatively easy to demonstrate is that dogs do give false signals that correspond to certain biases of the owners. Regardless of whether the last is true or not, the way we view detector dogs needs to be revisited in light of these clear biases. As it is, detector dogs seem to be barely better than dosing rods.