If they let him record public space and other's people property to prevent crime, than they can install their own cameras all over the town to do the same. I'm not sure many would be happy with that. I'm sure i wouldn't. He's free to record inside his property all he wants. Modern cameras allow you to black out at recording time parts of the footage. I do it on my cameras. I get all info i need on my own property and everyone else has their privacy no matter what.
It's slippery slope....you allow it here, than there, and before you know it, they are all over the place "because of the crime".