I've never had a company ask for proof of income and I wouldn't work at one that did. That's an insane requirement that should have nothing to do with whether or not I'm fit for the job and they're willing to pay what I ask for someone to do the job.
I am at a higher end of market salary range and when I tell potential recruiters my expectations and my previous salary they take my desires into account but ask for documentation.
There was a discussion here on HN a couple months ago that this approach is common in such cases.
sometimes they find out via other means. They're not supposed to be able to, but it happens. Other times they don't tell you until after it is too late.
