> Why is the business of the new employer to know how much I was making at my previous position?
This isn't the question that I answered. It was asked how stating a specific, untrue salary might be fraud.
Refusing to answer and giving an untrue number are different.
> Also, I could be wrong but I don't think a new employer will contact a previous employer to specifically learn how much a particular individual was earning.
Lying doesn't mean you'll get caught.
Also, be careful. For example, during a background check for one my jobs (a rather "ordinary" one), they said they couldn't verify one of my previous employers, and asked if I could send them proof. I sent W2s for both years I was employed and my offer letter, which satisfied them. Maybe some would feel that's too remote a risk to worry about, but it's not out of the question.