I would assume that the other company is pretty desperate for help, probably.
So even if Google or Microsoft or State Farm or <insert relevant industry leader for your job> was the person offering the job and saying they thought you're work was worth 20% more for them than where you currently are and nothing had to change, you'd decline because you'd assume they were just desperate and now adequately valuing your contributions? If another stable employer offered you 20% more, your first thought isn't "Hey, maybe that's how much I'm worth?"
Why are you excluding the part about going west? Albert may still have a home in St. Louis, but he'll be spending the majority of his time in Anaheim.
The question was about feeling underpaid. You can feel underpaid without needing to move cities for a new job. On these scales, relative to national big league players he was offered substantially more money and moving him up the list of highest paid players in history.
And I guess I assumed part of the reason you brought it up was Cost of Living or location desire. Not everyone likes California and not everyone likes St. Louis. So I was trying to take that subjectivity out of it. Also, as has been noted, Cost of Living adjustments are regressive. While the same house in LA will be substantially more expensive, the slight increase in other living costs likely won't dent his yearly salary like it would for you or I.
But if you can honestly tell me you wouldn't move to a different company next door or different department within your current company or that if someone was offering you 20% more than your current salary you wouldn't feel slightly underpaid then that answers my question. I'm isolating one thing; pay. Not morality, not ethics, location, commute, hours, responsibility, title, benefits, desirability.
My company has been really good to me for several years. I like my work, really enjoy the people I work with, and fully believe in the future of the company that I work for. All of those things are important to me.
Cost of living aside, I don't want to move. I like where I am at. An 18% pay increase would not be enough to make me start over with another company, in another part of the country.