This case has now made it back through the court system again. Obviously, the original facts haven't changed much. Since we last heard from our heroes, an evidentiary hearing in the district court has found that at the time of this stop Colorado temporary tags were not entered into CBI's database at all, so they would not have been available via an NCIC query. I could have told you that, but I work in Colorado. The trooper in this case works in Kansas, and so it's not surprising he didn't know that.
The prosecution changed tactics. Instead of arguing reasonable suspicion, they're now arguing that suppression is not an appropriate remedy. Basically, the exclusionary rule exists as a means to deter violations of the Fourth Amendment by removing any police incentive to conduct illegal searches. The exclusionary rule is a judicially created rule that isn't required (or even set forth) in the Constitution. So in cases where it would not fulfill its purpose (de-incentivising constitutional violations), it just not applied.
Short version: when the police are acting in good faith, and reasonably believe that they are doing things the right way, the exclusionary rule doesn't apply even if it is later determined that there was a violation of the Fourth Amendment.
That's what the prosecution was arguing for here: a ruling that the trooper in this case didn't know he was violating the Fourth Amendment. The Tenth Circuit assumed for the sake of argument that there was a violation of the Fourth Amendment, and ruled that if there was such a violation then it was in good faith and suppression was not an appropriate remedy.