It's not an idiotic line, it's just incomplete. They have a legal obligation to their shareholders demands, whether that be profits or otherwise. That is a simple fact that can't be disputed. It just happens that for most public companies, shareholders wan't short term profits.
This is worth parsing through slightly. CEO's have a fiduciary responsibility (not to act with malfeasance); and the shareholders have the right to replace the CEO. That's about it. The CEO is not under any obligation other than self-interest when it comes to what happens in between.
The meme about "profit maximization" is one of those Keynesian sayings "of a defunct economist" that seems to rule people's imaginations.
It's such an idiotic line and is usually given as a poor substitute for reasoning about a company's actions.