Being in that situation is so satisfying.

  Boss:      HR won't give me the money for your raise. 
  Employee:  I quit. I've been offered more money elsewhere. 
  Boss:      No wait actually I can get that extra money
  Employee:  Too late, kthxbai

+1 Never take a counter offer.

You'll get more pay but you're stuck in the same company run by the same narrow minds.

That's a rather narrow minded way to thinking about the issue.

I've accepted a counter offer twice, and both times I was glad that I did.

There could be many other reasons for a company not paying what you can get somewhere else. A very trivial one is the yearly update cycle: that may happen in January whereas you get an offer in June. Companies that hire don't align to the schedule of your current one.

And hiring companies inherently know asking somebody to quit and somewhere else carries a risk that needs some amount of kind of reward.

Hell, how can one personally even know what he/she is worth? There are so many factors at play. It'd be narrow minded to expect pricing perfection on something nobody really can get right.

Yes, but these are the narrow minds you know. Be sure there will be a new/different set of narrow minds at the next company.

In my experience narrow minds can be expanded.

Sure. If you need to seek out an offer every time you want to expand them, it's going to take a bit of work however.

All narrow minds can be expanded in theory. With an axe for example.

Plus they'll likely be looking to drop you in favour of someone they can play less soon after.

I'd like to strongly opposite to this advise.

You've got 2 companies you can work at. You should go to the one you prefer to work with. Maybe that's the one you already are in, maybe not.

Do what's best for yourself.

Never say never.

Some employers have special exemptions for counter-offers; your boss literally gets more money for your raise if you have a competing offer.

Not always the case. I did accept counter-offer and it worked out pretty well.