I'm Australian, and after hearing Stewart say that, I thought back on my own experiences. The only time I can recall it being used in a somewhat truthful manner is in an angry parental warning "Believe me, you're going to suffer if you continue that way" - some sort of threat that the person in question can carry out. Every other time, it's been bluster with no substance.

I mean seriously, if you throw out the question "Okay, who dropped the production database?" and one of the staff said "It wasn't me. Believe me!", that's kind of instant suspicion right there. It's a really weird thing to say in the contexts that Trump says it in.