No because on the google.com eula that you sign by having someone on your family ever Google something redeems them of any liability and gives them a right to sacrifice your first born to AI

If hypothetically when a false headline on a reputable site led to an incident involving injury or death, could Google is anyone found liable in anyway?

rarely

I doubt it.

Are you cooking something up?

They could hypothetically. Will they? Probably not.

Possibly. The BBC made a big row about Apple's headlines: https://www.bbc.com/news/articles/cx2v778x85yo