This is a form of hate and disgust against other people, probably because they judge the trash picking person as "disgusting, lazy, poor, homeless, trash, filth, scum" or whatever. They feel above the trash picker, so much so that they don't want the trash picking person to look or touch their garbage. Somehow, even their garbage is sacred.

Someone that hates another person so much that they would rather an item be destroyed then give it to another person needs to evaluate their heart and mind because clearly something is wrong there.

If a person uses the reason that they are worried about identity theft, they should shred their documents because hundreds of disposal employees have access to your trash on a daily basis. If you shred your documents, that issue is now solved.