It appears to be an urban myth. This was brought up in [the discussion on the answer][1] where repeated requests for sources were made. 


The blog post [6 Reasons Why Accepting A Counter Offer Is Madness][2] (linked in that discussion) investigates the claim.

>Despite considerable ferreting around the internet, I can’t find the source of that fact anywhere. I suspect it might be the result of a snap poll around a recruitment office somewhere, circa 2001, and it’s become accepted lore.


  [1]: https://chat.stackexchange.com/rooms/115990/discussion-on-answer-by-old-lamplighter-how-to-handle-counter-offer
  [2]: https://www.consultrecruitment.co.nz/blog/6-reasons-why-accepting-a-counter-offer-is-madness/