Of course. If you can come up with an intelligent counteroffer with a decent chance of success, then go ahead. It is, however, a failure of management to have had to make one. This may be why employees who take CO's often get fired; their existence is a continuing embarrassment to the manager who failed to promote/raise them until an ultimatum was made.
Which is exactly what I said in my comment. Treat the need for a counter offer as a failure, but don't just rule it out because the situation shouldn't have happened.
Before I was a manager, I believed that taking a counter offer was always stupid. Now that I'm on the other side of the fence, I see that it's not always so cut and dry. I wonder how many of the people supporting the author are actually managers in charge of compensation decisions.
I mean, startups usually fail. Does that mean one should never start a startup?