In search and rescue missions, the dog's handlers don't want false positives; they don't decide that they want to search a pile of rubble and then bring in a dog to justify it. If there's nothing in the rubble, they don't want to waste time searching. By contrast, in many cases where dogs alerts are used to justify a search, the police desire to perform the search precedes the dog's alert. Even if there's nothing for the dog to detect, many officers would still rather have the dog alert so as to justify their suspicions, than have the dog remain silent and thus let the suspects go.
What makes you believe bomb and drug dog handlers want false positives? I just can't see what there is to gain. If I'm a bird hunter and my bird dog is making false points one of us is doing something wrong and neither of us is going to be happy until the problem is remedied.