I believe that is correct. If my dog were "at-large" meaning unleashed and not fenced, and it was attacking someone on my property (perhaps me or another family member) and it could not be stopped by other means, the police could kill it. Though perhaps it could be argued that attacking its own family is not a "public" safety risk, but I think that would be a stretch.
However, they certainly couldn't kill it merely for being at-large either on my property or in the park. It needs to pose a public safety risk and be unstoppable by other means.
Please keep in mind, I'm not a lawyer, just doing my best to speak to the intent of what we passed.