Not necessarily true. I've worked with people who looked to leave, received offers from another company and then accepted counter offers to stay.

One ended up getting repeatedly promoted (so much so I wondered how he got promoted so fast, and only found out when I myself received a very generous counter offer as I was ready to jump ship), another got a very good counteroffer to stay and was subsequently pursued by the same company that he blew out by accepting a counteroffer at least twice more.

Ultimately if you're a good employee companies want the skillset. The only point I agree with in this article is that extra money doesn't make other problems go away, which is why I turned down a counteroffer even though it would have given me a 25% pay raise overnight.