Those animals had to be put down, and fast. They could not take the chance of them leaving the property and eating some kid at the morning bus stop 4 or 5 days later when they got really hungry. Public safety trumps animals....every single time.
Most tigers and lions you see in the zoo were born in captivity, as were their parents and grandparents. There is a reason that a big fense and mote surrounds those cages. There are lots of youtube videos that will show you what happens when a stupid human comes into contact with them.
This "tranquilizer argument" holds no water. How many local, rural, police departments keep and maintain tranquilizer guns? Really? Reports were that the closest tranquilizer guns were 20 minutes away. Well thats 40 minutes round trip. Are you going to ask Mr. Lion and Mr. Tiger who was just feeding on the head of their now dead care giver to not go anywhere?
If one of those beasts escaped and killed someone and I knew I could of put it down but didn't because I gave in to the politically correct culture I could not live with myself. Those cops did the right thing. Even the remote chance in the loss of human life alway trumps animal life. If you think any different you would change your mind if it was your kid that "got it" playing outside or at the bus stop.