Never underestimate the ability of people in power, but not in control, to paint themselves into a corner. The whole situation illustrates the pressures that the police feel, not to establish the truth, but to come up with plausible scapegoats. You could almost feel sorry for them if the consequences weren't so serious.
Why did it happen? Local pride, maybe, in not wanting to admit they were out of their depth; arrogance in believing that they could make the facts whatever they wanted them to be; and short-sightedness in terms of the prospects of maintaining their pretence indefinitely. All that, and confidence in their own impunity: the record of police officers being called to account in any meaningful way when the truth comes out in these cases, is pitiful.
Of course, the irony is that in these cases the usual result is that innocent people languish in jail while the real culprit has a free pass - which would have been the case here were it not for Lumumba's alibi (not for want of the Perugia police trying to act as if it didn't exist), and Guede's appearance in Germany.