Suppose that it's a fabrication. You could hire some independent company (e.g. Gallup or whoever) to conduct a confidential company-wide survey to determine how many employees have seen someone crying at their desk (or did so themselves), and approximately how many times in the past N years for some N. If the survey turned up results close to zero, that would support a case that the former employee is making it up. (Of course, subject to the limitation that the survey would only include current employees.)

There is also the principle that the burden of proof is on the one making a claim, and not on those who disbelieve. Lots of people cried on their desks? A few names, or it didn't happen.