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I believe it all depends on the managers/company, some take it little too personally, thats where things going to be sour forever and all of your insight is absolutely applicable. But there are instances where someone is actually an asset to an organization and even though the manager has the full honest intent to do all that he can to retain the resource, he is bind by the pay grade limitations, where situations like these (pre-counteroffer stage) gives an opportunity to raise some eyebrows in higher ranks and get stuff done out of the box.
But again, money isnt something going to keep folks motivated forever.