If someone is looking for a job elsewhere then they have already mentally left. They have chosen to leave and are in the process of doing so. To accept a counter offer means that either they didn't discuss their issues with the current job with their supervisor beforehand OR they did and nothing was done until an ultimatum was handed to them. The former is on the employee and is a risky prospect as there is no way to know if they employer is being fair or not. The later is on the employers and I would say never the time to accept a a counter offer.

If an offer comes out of the blue when someone isn't looking then, perhaps, it is reasonable for them to have a discussion with their current employer. If the employer cannot handle a mature discussion then it is time to leave whilst if they can then it is possible that both employee and employer want to maintain the status quo (with a mutually acceptable alteration in terms). Or the employer might negotiate a smoother exit e.g. long exit period.

In short, my guideline would be to never accept the counter off. But note that it is a guideline and under some circumstances it may be a reasonable situation to seriously consider it.