As with most stories, I'm sure there is more to it than what we've been privy to, but lets just take it on face value. First, the police were called, secondly they were physically challenged by someone brandishing a knife. Regardless if she was an 86 yr old grandma, if the officer attempted to physically remove the knife, there's a high probability that he would have been cut (how sever ?), in her presented state of mind. In a situation like this, no matter what the police do/attempt, they will be vilified. That's just the nature of the general public when offered these types of stories.
Now lets presume for a moment that the sweet old granny actual does lash out at the officer and connects with neck and the artery is severed. Now we have a really nasty byline for some reported, but what happens to granny.......nothing. She would have been deemed mentally incompetent and would be in a hospital, as for the officer, well most likely he doesn't go home to the wife and kids. It's very easy for folks to sit back and reflect on an incident, lawyers and judges also, but the officer has to make a split second decision that follows him for his whole life. He doesn't have the luxury to mull over possible options, if any in a situation, but he's expected/tasked by the public to make these decisions, if he doesn't then he's under investigation by his department and that can/could lead to being demoted/fired or even indicted, depending upon the situation.
Bottom line to this particular story is granny's apparently fine, no worse for the wear and the cops will just have to bear another flogging at the hands of the media.