Signing that petition isn't just a doubt. It's a statement that you do not believe it exists. There is no doubt, you "know" it isn't true.
I recall the spokesman for the former Iraqi government making statements like "We have driven the American dogs out of our homeland. Our fields are now watered in their blood. We have easily defeated their pitiful forces." and on and on as the US was taking Baghdad.
I remember hearing reports of the passengers of the Titanic steadfastly refusing to believe there was anything wrong until they were ordered into life boats.
Rejecting global climate change outright is just like my the people who call us crazy because "nothing is ever going to happen."
Conversely, just because a bunch of people say the sky is falling doesn't mean it is. Look at the War Of The Worlds panic in the 50's.