but what's more important: a short detainment of innocent individuals, or catching a violent criminal?The fact that you're asking this shows that: You have no concept of what the Bill of Rights means and that you were born 60 years too late and in the wrong country
Would you give up 10 minutes of freedom in order to get this guy off the street?
Nope - not 10 seconds. Have you heard of William Blackstone? "Better that ten guilty persons escape than that one innocent suffer,"
You're missing the point. You usually do. If the cops had very good, reliable info that meets the reasonable suspicion standard (you don't need probable cause in this case), then they have the right to do what they did.
We don't know what their 'reliable' info was, however. If it was, in fact, a GPS device in the stolen money, then searching the immediate area would probably be a good search. We need all the info, but we don't have it. I, unlike you, do not jump to radical conclusions to fit my own views.