Emergency vehicles will always have the right away, even during a film shoot. So the police vehicle had every right to go down a closed street.
But I think the cop used poor judgement. Not knowing what to expect, he or she jeopordized their response time by taking an extra minute by going around the detour to not even making it to the call.
What if the vehicles were reversed? Meaning that it was the big truck that was travelling down the same path as the car?
I think this would make a great training video for reminding cops to use their best judgement. If I called 911, and needed a cop to show up ASAP, I certainly want them to arrive as earliest as possible, but not to a point that they take unneccessary risks that they end up not showing up at all.