Thinking further, how would you even know that a claimed job offer is authentic, and not just a ploy to get a raise? You wouldn't be able to call the alleged new place up to ask.

What if the employee continues to shop, looking for even higher offers to game the system? Will you give them a raise each time?

This is assuming that not everybody is honest or completely ethical when it comes to money. I'm not really alarmist, but I wouldn't invite this kind of unverifiable abuse, either.