Ya know, after I had written my parallel comment and gave it some thought later, I concluded that it's all just bullshit. The dog didn't alert by sitting, and the officer didn't cue him. They were going to search the car regardless.
You say 'no', but, the puppy says 'yes' and there go your rights. It is pretty magic.
Here's where I disagree with you (but only in the details). The dog didn't say anything. I mean, I've seen dogs sniff for drugs (and find them). I've watched amateur Noseworks competitors (slightly related to the training sniffing dogs). No dog "alerts" by sitting, at least none I've ever seen. Dogs sit all the time, it would be a stupid cue. That dog could have just stood there and ripped the meanest fart you ever smelled, and the thieves (pardon: cops) would have said that the dog "alerted". "Yup, smells like he found something!"
As you point out, the dog is a prop, a talisman. That car was getting searched, full stop. They just needed a "get out of the 4th amendment free" card in the shape of a German Shepherd. They might as well train gerbils for that. They fit in your pocket, cost less to feed, and with a little propaganda we can all be led to believe they work just as well as dogs (and they probably will if you're just looking for false positives).
(And to be clear, I'm not saying you can't train a dog to sniff for drugs or bombs. Obviously they can be trained for this, and to a high degree of reliability. They can, however, also be trained to bark, dig, or whine on command, whether they smell drugs or not.)