That is where I said "unless their principal business is not risk". Having said that
Stone v. Ritter [Delaware 2006], while the court found on behalf of the company because the issue at hand was whether a failure to institute a particular program of internal corporate espionage to detect malfeasance or malpractice by its employees constituted liability upon its directors (the court found that in the instant case it did not), it did state that under a corporation's fiduciary duties is the duty of loyalty.
Stone v. Ritter cites Guth V. Loft [Delware 1939] in helping characterize that the duty of loyalty
...demands of a corporate officer or director, peremptorily and inexorably, the most scrupulous observance of his duty, not only affirmatively to protect the interests of the corporation committed to his charge, but also to refrain from anything that would work injury to the corporation, or to deprive it of profit or advantage which his skill and ability might properly bring to it, or to enable it to make in the reasonable and lawful exercise of its powers.
So while the courts do give wide latitude to directors to make decisions on behalf of their companies, to include significant propositions of risk, it is clear that there is some threshold at which a reasonable level of risk crosses over into territory that constitutes a violation of the Duty of Loyalty as it posses a likelihood to
... work injury to the corporation, or to deprive it of profit or advantage...
Under that guidance, a corporate officer needs to be able to show that their decisions pose a reasonable likelihood of being profitable to the company (conceding that what constitutes reasonable is generally quite broad).
So you are correct to say, in as much as I can find, that there is no such law, but there is such guiding principal which colors the law and the rulings of the courts and, more importantly to corporate directors, the disposition of shareholders. If you are tossed from your directorate position by a shareholder led initiative, or have to spend months or years fighting to defend a decision that you made because of the same, do the semantics of the process really matter? Does that not work to seriously disincentivize actions that are more likely to fail than to succeed?
Again, you are correct that a company is more tightly bound to abide by its articles of incorporation. Somethings, however, won't fly. You could file as a non-profit (though we aren't talking about non-profits here) but generally you must turn a profit some percentage of years (3 of last 5) or demonstrate that you can turn a profit or basically, show that the business is viable in order to receive tax deductions for expenses. There is a window of opportunity where start-ups can by-pass these requirements, but eventually you will be relegated to hobby status, and my recollection is that some states will rescind your articles of incorporation if you fail to demonstrate viability for X period of time. All this ignores the fact that exactly what kind of IPO or valuation do you think a company is going to have when their 10Ks say they don't intend to make a profit? You drop that valuation too far, particularly in technology rich turf such as space exploration, and you are some other company's lunch, and if you are public there isn't a damn thing you can do about it. So this all leaves you back at the wealthy individual territory which we previously covered.
Lastly, with respect to your example of SpaceX, the regulatory bodies (both public and private) place certain profitability and market capitalization requirements on corporations as a requirement for listing on exchanges. Even if SpaceX makes those requirements (and it looks like they may well be near that) they have to maintain them to some degree after IPO. That means hugely costly efforts that would deplete market cap are almost certainly not possible. Elon Musk has basically said the same thing, and that's part of the reason he hasn't taken SpaceX public.
Valid points, but I think the distinction is that if the general public wants a business to take on debt to perform some function for the public, well that ain't going to happen unless the shareholders want it. Shareholders are shareholders because they want to turn a profit, preferably quickly; they tend to have a dim opinion of things with an unknown return potential at some vaguely distant time in the future with a quantifiably negative impact on dividends in the near term. That's the trade-off of public investment.
However, if the public wants such a program to happen (and I'm making no statement about whether that's the case or not here), then it is usually something that a government is logistically more able (though not necessarily more capable) to do. That said, you are correct in that there needs to be some weenie, some potential payoff for the investment in one form or another, regardless of whether it is a public or private (or hybrid) program. The differentiator is that the confidence threshold for payoff for a government is generally much lower than that for a publicly traded business (particularly when the investment is huge).
Sensitive much? There was nothing anti-business about what NDT said. He stated simply as fact, the exact same rational that pundits on the right-hand side of spectrum have used repeatedly when explaining why business-oriented individuals are better candidates to run the government: businesses are results oriented, and generally risk averse. If they are publicly traded and their principal business is not risk, then they are required to be by law.
Tyson wasn't making a qualitative statement about business competence or capability, he was talking about the fact that there is not even the teeniest tiniest business case that can be made for building a human spaceflight program to Mars. None. No CxO could present such a proposition to their board without running the very real risk of receiving a vote of no-confidence. This is fact, not the bias of a left-wing statist (though ad hominem is clearly the appropriate mechanism through which to debate your point and win people to your position).
Now, could a counter argument be made to NDT's point that perhaps a single, very rich, individual might be able to accomplish such a feat without having to worry about the ROI implications, perhaps even more nimbly and efficiently than governmental bureaucracy would allow? Sure, and I believe that Elon Musk is exactly that type of individual. Though I suspect that even he doesn't have the resources to pull it off alone, and will need outside investment. Which brings us back to challenges faced by business that Tyson identified.
Argue your position. Stop with the my team/your team red vs. blue bullshit and engage in an honest debate. If we don't find a way to do this as a society, to step away from demagoguery and ideological obstinence in order to find consensus, or at least rational, well-reasoned disagreement, then we have much, much bigger existential problems to address than the challenges presented by a manned mission to Mars.
The answer to the question of Life, the Universe, and Everything is... Four day work week, Two ply toilet paper!