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.
I would never work for a company that went to that level. In 10 years, I havent seen a company pull that. If you suspect that might be part of their hiring process. Just say "I need to make X" and evade all talk of current salary.
As I mentioned in previous comment - companies would do this in case they really want a candidate but feel that previous compensation is somewhat above the market. They OK to pay market rate (if you can prove that) but are weary that a candidate employs the strategy suggested by the parent comment. I this case showing proof of previous compensation usually helps with negotiations.
In countries where the employer does the tax for the employee, then the employer will see how much tax has been paid earlier in the year. They can deduce salary from that.