The myth comes in where people believe that means the burden of proof is such that they have to blindly serve short term financial interests of shareholders. There is no such rule at all, in fact it's quite the opposite:

https://en.wikipedia.org/wiki/Business_judgment_rule

The business judgment rule is a case law-derived doctrine in corporations law that courts defer to the business judgment of corporate executives. It is rooted in the principle that the "directors of a corporation... are clothed with [the] presumption, which the law accords to them, of being [motivated] in their conduct by a bona fide regard for the interests of the corporation whose affairs the stockholders have committed to their charge".[1] The rule exists in some form in most common law countries, including the United States,[1] Canada,[2] England and Wales,[3] and Australia.[4]

To challenge the actions of a corporation's board of directors, a plaintiff assumes "the burden of providing evidence that directors, in reaching their challenged decision, breached any one of the triads of their fiduciary duty — good faith, loyalty, or due care".[5] Failing to do so, a plaintiff "is not entitled to any remedy unless the transaction constitutes waste... [that is,] the exchange was so one-sided that no business person of ordinary, sound judgment could conclude that the corporation has received adequate consideration".