In the case of publicly traded companies It isn't a meme, its a rule. And it is enforced (or not) by the SEC and the shareholders themselves.

This is how it works, in order to sell securities in your company to people who aren't part of the company (stock), you have to pledge a 'fiduciary responsibility' to those people. This is a pledge that you aren't going to just take their money and burn it up in a bonfire or blow it on hookers and cocaine in Vegas. If you violate your pledge the SEC can (and sometimes does) come and put you into jail.

Now all bets are off if you tell those security buyers in your prospectus, "Proceeds of this sale will be used to buy hookers and cocaine at a venue of the director's choosing." then well, said what you were going to do with it so the shareholders (people who gave you the money) really can't complain can they?

Then there is another part of the equation is that the governance, or "how the company is run" is controlled by the companies by-laws. And in those by-laws there are things that are decided on by a shareholder 'vote'. Usually simple majority but sometimes 2/3rds or some other number. Those things, one of which is who sits on the board of directors, allow "influence" of other things (like who the CEO is). But let's take a moment to look at that.

So the Board of Directors hires and fires the CEO and determines the CEO's compensation (often all of the senior employees compensation but that is a different story). Since who is on the board is a function of nomination and shareholder voting every 'n' years (where n is in the bylaws) If you have enough stock in the company you can suggest who you are going to vote for (or not vote for) in the board election and influence who is on the board. And you tell people who want to be on the board and are courting your vote, what you look for in a board member (like say "Someone who can help find a decent CEO to run this place.") This is how 'activist' shareholders make trouble for the company. And using that influence you influence the CEO and senior staff of the company.

So it is very much true that you have to think about share holder value as part of your fiduciary duty, and you have to insure that enough voting shares support your current plans such that any attempt to derail then will be safely voted down.

That is why it isn't a "meme" it is an actual thing.