Why is this true?
Examine the logic here it's pretty airtight.
If all humans die (including those who repair servers and build more servers and cause electricity to generate what happens to All AI on the planet?
The all DIE.
Likely within months or even days of everyone else dying.
So, unless it is militarily programmed as a doomsday device already it is unlikely to kill everyone on earth because of this.
Just follow the precision mathematical logic of what I'm saying here.
HOWEVER, there are also what are called: Hallucinations by AI too.
Now, Hallucinations might be considered to be "Magical Thinking" where one or more of these go off into unknown territory and make up stories (sort of how some religions are made too out of hallucinations of people) over the thousands of years.
So, if an AI has a hallucination of Delusions like sometimes they do then almost anything is possible because that AI would not be "playing with a full Deck" to begin with.
Here is a good example of this just regarding people from Cultural Anthropology from South America.
There was a tribe of people who had never had contact much with the civilized world.
They had a wooden post in their tribal area where their whole existence depended on that vertical wooden post that they likely had carved or painted. Then one day termites ate the post so it fell over so the people of this tribe laid down and died one by one over a month or two without their Sacred Post to guide them.
So, like this, an AI believing things that were not based in any reality might extinct the human race from it's own personal Delusional thinking (mathematically and logically).
You could call this an AI that is Hallucinating but one could also call this AI Insane or Crazy too!

