Sure, and the upside is a strengthened position as a prospective employee. As an employee or prospective employee to a new organization, what's the downside?
If you are currently underpaid, it could reduce you leverage with the prospective employer. I have 2Xed my pay because a new employer didn't know my current rate.
Given the amount of tracking that's possible today, I think that anybody who cared would be able to easily determine your exact salary if the salary of every position at a company were published.