There isn’t too much more to elaborate on, it simply isn’t the case, but it is such a common thing to say that it is worth researching. You’ll hear the 1919 case “Dodge v Ford” brought up as proof, one good place to start reading is the Wikipedia “Significance” section and the associated citations, as they go deeper into the subject than just that single case.
There simply is no interpretation of “fiduciary duty” that requires “maximization of shareholder value” outside of the misinformed lay person discussion of the subject.
You can even just logically see why such an interpretation would be impossible: given N shareholders all with different interests and different financial situations, how do you even define “maximizing their value” and what time duration are you basing that off? Imagine how absurd the courts would be if such a statute did exist: you’d have people owning 1 share in a company suing the company because it did something that wasn’t maximizing “value” as they define it.
The reality is that the business judgement rule is case law and is often cited and is often used as defenses against such assertions.