Suppose the handler was pure as the driven snow, had a Dolittle-like ability to talk with the animals, and Rover's senses performed exactly as advertised: It is still a statistical impossibility for $12,000 in American paper money to not contain traces of dope. Dope-residue-as-probable-cause is just a license to confiscate.
Forget the dog. The dog is a Red Herringhound.
Suppose instead of the dog, they’d used one of dozens of chemical dye tests and found dope residue on the money. Does taking Fluffy the Crotch-Sniffing Four-Legged Fourth Amendment expert out of the picture make it any more right?